fbpx
Wikipedia

Expansion of the universe

May 04, 2023

The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time.[1] It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. This expansion involves neither space nor objects in space "moving" in a traditional sense, but rather it is the metric (which governs the size and geometry of spacetime itself) that changes in scale. As the spatial part of the universe's spacetime metric increases in scale, objects become more distant from one another at ever-increasing speeds. To any observer in the universe, it appears that all of space is expanding, and that all but the nearest galaxies (which are bound by gravity) recede at speeds that are proportional to their distance from the observer. While objects within space cannot travel faster than light, this limitation does not apply to the effects of changes in the metric itself.[notes 1] Objects that recede beyond the cosmic event horizon will eventually become unobservable, as no new light from them will be capable of overcoming the universe's expansion, limiting the size of our observable universe.

As an effect of general relativity, the expansion of the universe is different from the expansions and explosions seen in daily life. It is a property of the universe as a whole and occurs throughout the universe, rather than happening just to one part of the universe. Therefore, unlike other expansions and explosions, it cannot be observed from "outside" of it; it is believed that there is no "outside" to observe from.

Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann–Lemaître–Robertson–Walker metric and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above), because gravity binds matter together strongly enough that metric expansion cannot be observed on a smaller scale at this time. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the universe given the matter density and average expansion rate.

According to inflation theory, during the inflationary epoch about 10−32 of a second after the Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 1078 (an expansion of distance by a factor of at least 1026 in each of the three dimensions). This would be equivalent to expanding an object 1 nanometer (10−9 m, about half the width of a molecule of DNA) in length to one approximately 10.6 light years (about 1017 m or 62 trillion miles) long. A much slower and gradual expansion of space continued after this, until at around 9.8 billion years after the Big Bang (4 billion years ago) it began to gradually expand more quickly, and is still doing so. Physicists have postulated the existence of dark energy, appearing as a cosmological constant in the simplest gravitational models, as a way to explain this late-time acceleration. According to the simplest extrapolation of the currently favored cosmological model, the Lambda-CDM model, this acceleration becomes more dominant into the future. In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope.[2]

History

In 1912, Vesto Slipher discovered that light from remote galaxies was redshifted,[3][4] which was later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding.[5]

Swedish astronomer Knut Lundmark was the first person to find observational evidence for expansion in 1924. According to Ian Steer of the NASA/IPAC Extragalactic Database of Galaxy Distances, "Lundmark's extragalactic distance estimates were far more accurate than Hubble's, consistent with an expansion rate (Hubble constant) that was within 1% of the best measurements today."[6]

In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented observational evidence for a linear relationship between distance to galaxies and their recessional velocity.[7] Edwin Hubble observationally confirmed Lundmark's and Lemaître's findings in 1929.[8] Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other.

Astronomer Walter Baade recalculated the size of the known universe in the 1940s, doubling the previous calculation made by Hubble in 1929.[9][10][11] He announced this finding to considerable astonishment at the 1952 meeting of the International Astronomical Union in Rome. For most of the second half of the 20th century, the value of the Hubble constant was estimated to be between 50 and 90 (km/s)/Mpc.

Based on large quantities of experimental observation and theoretical work, the scientific consensus is that space itself is expanding, and that it expanded very rapidly within the first fraction of a second after the Big Bang, approximately 13.8 billion years ago. This kind of expansion is known as "metric expansion". In mathematics and physics, a "metric" means a measure of distance, and the term implies that the sense of distance within the universe is itself changing.

On 13 January 1994, NASA formally announced a completion of its repairs on the main mirror of the Hubble Space Telescope allowing for sharper images and, consequently, more accurate analyses of its observations.[12] Briefly after the repairs were made, Wendy Freedman's 1994 Key Project analyzed the recession velocity of M100 from the core of the Virgo cluster, offering a Hubble constant measurement of 80±17 km s-1 Mpc-1 (Mega Parsec).[13] Later the same year, Adam Riess et al utilized an empirical method of visual band light shape curves to more finely estimate the luminosity of Type Ia supernova. This further minimized the systemic measurement errors of the Hubble constant to 67±7 km s-1 Mpc-1. Reiss's measurements on the recession velocity of the nearby Virgo cluster more closely agree with subsequent and independent analyses of Cepheid variable calibrations of 1a supernovae, which estimates a Hubble Constant of 73±7km s-1 Mpc-1.[14] Within the next decade, in 2003, David Spergel's analysis of the Cosmic microwave background during the first year observations of the Wilkinson Microwave Anisotropy Probe satellite (WMAP) further agreed with the estimated expansion rates for local galaxies, 72±5 km s-1 Mpc-1.[15]

Cosmic inflation

Main articles: inflation (cosmology) and inflaton

The modern explanation for the metric expansion of space was proposed by physicist Alan Guth in 1979 while investigating the problem of why no magnetic monopoles are seen today. Guth found in his investigation that if the universe contained a field that has a positive-energy false vacuum state, then according to general relativity it would generate an exponential expansion of space. It was very quickly realized that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look as it does today, the universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation theory largely resolves these problems as well, thus making a universe like ours much more likely in the context of Big Bang theory. According to Roger Penrose, inflation does not solve the main problem it was supposed to solve, namely the incredibly low entropy (with unlikeliness of the state on the order of 1/1010128 ⁠) of the early Universe contained in the gravitational conformal degrees of freedom (in contrast to fields degrees of freedom, such like the cosmic microwave background whose smoothness can be explained by inflation). Thus, he puts forward his scenario of the evolution of the Universe: conformal cyclic cosmology.[16]

No field responsible for cosmic inflation has been discovered. However such a field, if found in the future, would be scalar. The first similar scalar field proven to exist was only discovered in 2012–2013 and is still being researched. So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered.[citation needed]

The proposed field and its quanta (the subatomic particles related to it) have been named inflaton. If this field did not exist, scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred, and is still occurring much more slowly today.

Overview of metrics and comoving coordinates

Main articles: Metric (mathematics) and tensor

To understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.

A metric defines the concept of distance, by stating in mathematical terms how distances between two nearby points in space are measured, in terms of the coordinate system. Coordinate systems locate points in a space (of whatever number of dimensions) by assigning unique positions on a grid, known as coordinates, to each point. Latitude and longitude, and x-y graphs are common examples of coordinates. A metric is a formula that describes how a number known as "distance" is to be measured between two points.

It may seem obvious that distance is measured by a straight line, but in many cases it is not. For example, long haul aircraft travel along a curve known as a "great circle" and not a straight line, because that is a better metric for air travel. (A straight line would go through the earth). Another example is planning a car journey, where one might want the shortest journey in terms of travel time - in that case a straight line is a poor choice of metric because the shortest distance by road is not normally a straight line, and even the path nearest to a straight line will not necessarily be the quickest. A final example is the internet, where even for nearby towns, the quickest route for data can be via major connections that go across the country and back again. In this case the metric used will be the shortest time that data takes to travel between two points on the network.

In cosmology, we cannot use a ruler to measure metric expansion, because our ruler's internal forces easily overcome the extremely slow expansion of space, leaving the ruler intact. Also, any objects on or near earth that we might measure are being held together or pushed apart by several forces that are far larger in their effects. So even if we could measure the tiny expansion that is still happening, we would not notice the change on a small scale or in everyday life. On a large intergalactic scale, we can use other tests of distance and these do show that space is expanding, even if a ruler on earth could not measure it.

The metric expansion of space is described using the mathematics of metric tensors. The coordinate system we use is called "comoving coordinates", a type of coordinate system that takes account of time as well as space and the speed of light, and allows us to incorporate the effects of both general and special relativity.

Example: "Great Circle" metric for Earth's surface

For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of spherical geometry. Because the surface of the Earth is two-dimensional, points on the surface of the Earth can be specified by two coordinates – for example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude, or X-Y-Z Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in long-haul airline flights where the distance between two points is measured based upon a great circle, rather than the straight line one might plot on a two-dimensional map of the Earth's surface. In general, such shortest-distance paths are called "geodesics". In Euclidean geometry, the geodesic is a straight line, while in non-Euclidean geometry such as on the Earth's surface, this is not the case. Indeed, even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth. The difference between the straight line path and the shortest-distance great circle path is due to the curvature of the Earth's surface. While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.

On plane maps, great circles of the Earth are mostly not shown as straight lines. Indeed, there is a seldom-used map projection, namely the gnomonic projection, where all great circles are shown as straight lines, but in this projection, the distance scale varies very much in different areas. There is no map projection in which the distance between any two points on Earth, measured along the great circle geodesics, is directly proportional to their distance on the map; such accuracy is possible only with a globe.

Metric tensors

In differential geometry, the backbone mathematics for general relativity, a metric tensor can be defined that precisely characterizes the space being described by explaining the way distances should be measured in every possible direction. General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame. This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated.

A metric expansion occurs when the metric tensor changes with time (and, specifically, whenever the spatial part of the metric gets larger as time goes forward). This kind of expansion is different from all kinds of expansions and explosions commonly seen in nature in no small part because times and distances are not the same in all reference frames, but are instead subject to change. A useful visualization is, rather than imagining objects in a fixed "space" moving apart into "emptiness", instead imagine space itself growing between all objects, without any acceleration or movement of the objects themselves. The space between objects shrinks or grows as the various geodesics converge or diverge.

Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.

Theory and observations suggest that very early in the history of the universe, there was an inflationary phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called Hubble expansion, the moving apart of all gravitationally unbound objects in the universe. The expanding universe is therefore a fundamental feature of the universe we inhabit – a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory.

Comoving coordinates

Main article: Comoving coordinates

In expanding space, proper distances are dynamical quantities that change with time. An easy way to correct for this is to use comoving coordinates, which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation. Any time-evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations in addition to any other effects that may be operating (gravity, dark energy, or curvature, for example). Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for observational cosmology.

Understanding the expansion of the universe

Measurement of expansion and change of rate of expansion

 
When an object is receding, its light gets stretched (redshifted). When the object is approaching, its light gets compressed (blueshifted).

In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans. The expansion of space is measured indirectly. The theory of relativity predicts phenomena associated with the expansion, notably the redshift-versus-distance relationship known as Hubble's Law; functional forms for cosmological distance measurements that differ from what would be expected if space were not expanding; and an observable change in the matter and energy density of the universe seen at different lookback times.

The first measurement of the expansion of space came with Hubble's realization of the velocity vs. redshift relation. Most recently, by comparing the apparent brightness of distant standard candles to the redshift of their host galaxies, the expansion rate of the universe has been measured to be H0 = 73.24 ± 1.74 (km/s)/Mpc.[17] This means that for every million parsecs of distance from the observer, the light received from that distance is cosmologically redshifted by about 73 kilometres per second (160,000 mph). On the other hand, by assuming a cosmological model, e.g. Lambda-CDM model, one can infer the Hubble constant from the size of the largest fluctuations seen in the Cosmic Microwave Background. A higher Hubble constant would imply a smaller characteristic size of CMB fluctuations, and vice versa. The Planck collaboration measure the expansion rate this way and determine H0 = 67.4 ± 0.5 (km/s)/Mpc.[18] There is a disagreement between the two measurements, the distance ladder being model-independent and the CMB measurement depending on the fitted model, which hints at new physics beyond our standard cosmological models.

The Hubble parameter is not thought to be constant through time. There are dynamical forces acting on the particles in the universe that affect the expansion rate. It was earlier expected that the Hubble parameter would be decreasing as time went on due to the influence of gravitational interactions in the universe, and thus there is an additional observable quantity in the universe called the deceleration parameter, which cosmologists expected to be directly related to the matter density of the universe. Surprisingly, the deceleration parameter was measured by two different groups to be less than zero (actually, consistent with −1), which implied that today the Hubble parameter is converging to a constant value as time goes on. Some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic jerk".[19] The 2011 Nobel Prize in Physics was given for the discovery of this phenomenon.[20]

In October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble Constant, essential in establishing the rate of expansion of the universe.[21][22]

Measuring distances in expanding space

 
 
Two views of an isometric embedding of part of the visible universe over most of its history, showing how a light ray (red line) can travel an effective distance of 28 billion light years (orange line) in just 13 billion years of cosmological time. (Mathematical details)

At cosmological scales, the present universe conforms to Euclidean space, what cosmologists describe as geometrically flat, to within experimental error.[23]

Consequently, the rules of Euclidean geometry associated with Euclid's fifth postulate hold in the present universe in 3D space. It is, however, possible that the geometry of past 3D space could have been highly curved. The curvature of space is often modeled using a non-zero Riemann curvature tensor in Curvature of Riemannian manifolds. Euclidean "geometrically flat" space has a Riemann curvature tensor of zero.

"Geometrically flat" space has 3 dimensions and is consistent with Euclidean space. However, spacetime on the other hand, is 4 dimensions; it is not flat according to Einsten's general theory of relativity. Einstein's theory postulates that "matter and energy curve spacetime, and there are enough matter and energy lying around to provide for curvature."[24]

In part to accommodate such different geometries, the expansion of the universe is inherently general relativistic. It cannot be modeled with special relativity alone: though such models exist, they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe.

The images to the right show two views of spacetime diagrams that show the large-scale geometry of the universe according to the ΛCDM cosmological model. Two of the dimensions of space are omitted, leaving one dimension of space (the dimension that grows as the cone gets larger) and one of time (the dimension that proceeds "up" the cone's surface). The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the Big Bang, while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion as a splaying outward of the spacetime, a feature that eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the Big Bang. The cyan grid lines mark off comoving distance at intervals of one billion light years in the present era (less in the past and more in the future). Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely for illustrative purposes; a flat universe does not curl back onto itself. (A similar effect can be seen in the tubular shape of the pseudosphere.)

The brown line on the diagram is the worldline of Earth (or more precisely its location in space, even before it was formed). The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching Earth at the present day. The orange line shows the present-day distance between the quasar and Earth, about 28 billion light years, which is a larger distance than the age of the universe multiplied by the speed of light, ct.

According to the equivalence principle of general relativity, the rules of special relativity are locally valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed c; in the diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance ct in a time t, as the red worldline illustrates. While it always moves locally at c, its time in transit (about 13 billion years) is not related to the distance traveled in any simple way, since the universe expands as the light beam traverses space and time. The distance traveled is thus inherently ambiguous because of the changing scale of the universe. Nevertheless, there are two distances that appear to be physically meaningful: the distance between Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension defined as the spatial dimension). The former distance is about 4 billion light years, much smaller than ct, whereas the latter distance (shown by the orange line) is about 28 billion light years, much larger than ct. In other words, if space were not expanding today, it would take 28 billion years for light to travel between Earth and the quasar, while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.

The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away. In fact, the light emitted towards Earth was actually moving away from Earth when it was first emitted; the metric distance to Earth increased with cosmological time for the first few billion years of its travel time, also indicating that the expansion of space between Earth and the quasar at the early time was faster than the speed of light. None of this behavior originates from a special property of metric expansion, but rather from local principles of special relativity integrated over a curved surface.

Topology of expanding space

 
A graphical representation of the expansion of the universe from the Big Bang to the present day, with the inflationary epoch represented as the dramatic expansion of the metric seen on the left. This visualization can be confusing because it appears as if the universe is expanding into a pre-existing empty space over time. Instead, the expansion created, and continues to create, all of known space and time.

Over time, the space that makes up the universe is expanding. The words 'space' and 'universe', sometimes used interchangeably, have distinct meanings in this context. Here 'space' is a mathematical concept that stands for the three-dimensional manifold into which our respective positions are embedded while 'universe' refers to everything that exists including the matter and energy in space, the extra-dimensions that may be wrapped up in various strings, and the time through which various events take place. The expansion of space is in reference to this 3-D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.[25]

The ultimate topology of space is a posteriori – something that in principle must be observed – as there are no constraints that can simply be reasoned out (in other words there can not be any a priori constraints) on how the space in which we live is connected or whether it wraps around on itself as a compact space. Though certain cosmological models such as Gödel's universe even permit bizarre worldlines that intersect with themselves, ultimately the question as to whether we are in something like a "Pac-Man universe" where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon (or a planet like the Earth) is an observational question that is constrained as measurable or non-measurable by the universe's global geometry. At present, observations are consistent with the universe being infinite in extent and simply connected, though we are limited in distinguishing between simple and more complicated proposals by cosmological horizons. The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe, and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.[26]

Regardless of the overall shape of the universe, the question of what the universe is expanding into is one that does not require an answer according to the theories that describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands.

Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite.

Density of universe during expansion

Despite being extremely dense when very young and during part of its early expansion – far denser than is usually required to form a black hole – the universe did not re-collapse into a black hole. This is because commonly used calculations for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as the Big Bang.

Effects of expansion on small scales

The expansion of space is sometimes described as a force that acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant, it is not an accurate picture of the phenomenon of expansion in general.[27]

 
Animation of an expanding raisin bread model. As the bread doubles in width (depth and length), the distances between raisins also double.

In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so.

There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter.

Once objects are bound by gravity, they no longer recede from each other. Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling towards us and is not expanding away. Within the Local Group, the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place. Once one goes beyond the Local Group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the "Hubble Flow" and end up as bound, non-expanding objects up to the scales of superclusters of galaxies. We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled. Currently, the Local Group is being gravitationally pulled towards either the Shapley Supercluster or the "Great Attractor" with which, if dark energy were not acting, we would eventually merge and no longer see expand away from us after such a time.

A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the FLRW geometry, the same geometry that describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe, which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed c with respect to the local motion of the exploding matter, a phenomenon analogous to frame dragging.

The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a vacuum energy density has the effect of adding a repulsive force between objects that is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects that have clumped together under the influence of gravity, and even on individual atoms. However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state that is slightly (undetectably) larger than it would otherwise have been. As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases. Thus, the ultimate fate of the ΛCDM universe is a near vacuum expanding at an ever-increasing rate under the influence of the cosmological constant. However, the only locally visible effect of the accelerating expansion is the disappearance (by runaway redshift) of distant galaxies. Gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time. It is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby Virgo Cluster. However, galaxies lying farther away from this will recede away at ever-increasing speed and be redshifted out of our range of visibility.

Metric expansion and speed of light

At the end of the early universe's inflationary period, all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principle and Einstein's general theory of relativity and this is when the precise and regular form of the universe's expansion had its origin (that is, matter in the universe is separating because it was separating in the past due to the inflaton field).[citation needed]

While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging, it does not apply to situations where spacetime curvature or evolution in time become important. These situations are described by general relativity, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame. The definition of distance used here is the summation or integration of local comoving distances, all done at constant local proper time. For example, galaxies that are farther than the Hubble radius, approximately 4.5 gigaparsecs or 14.7 billion light-years, away from us have a recession speed that is faster than the speed of light. Visibility of these objects depends on the exact expansion history of the universe. Light that is emitted today from galaxies beyond the more-distant cosmological event horizon, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past. Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.[28] Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within the fields of education and communication of scientific concepts.[29][30][31][32]

Scale factor

At a fundamental level, the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe. The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below. This feature of the universe can be characterized by a single parameter that is called the scale factor, which is a function of time and a single value for all of space at any instant (if the scale factor were a function of space, this would violate the cosmological principle). By convention, the scale factor is set to be unity at the present time and, because the universe is expanding, is smaller in the past and larger in the future. Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero; our current understanding of cosmology sets this time at 13.787 ± 0.020 billion years ago. If the universe continues to expand forever, the scale factor will approach infinity in the future. In principle, there is no reason that the expansion of the universe must be monotonic and there are models where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion.

Other conceptual models of expansion

The expansion of space is often illustrated with conceptual models that show only the size of space at a particular time, leaving the dimension of time implicit.

In the "ant on a rubber rope model" one imagines an ant (idealized as pointlike) crawling at a constant speed on a perfectly elastic rope that is constantly stretching. If we stretch the rope in accordance with the ΛCDM scale factor and think of the ant's speed as the speed of light, then this analogy is numerically accurate – the ant's position over time will match the path of the red line on the embedding diagram above.

In the "rubber sheet model" one replaces the rope with a flat two-dimensional rubber sheet that expands uniformly in all directions. The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet.

In the "balloon model" the flat sheet is replaced by a spherical balloon that is inflated from an initial size of zero (representing the big bang). A balloon has positive Gaussian curvature while observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation. This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time.

In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely grow farther away from each other.

Theoretical basis and first evidence

 
The expansion of the universe proceeds in all directions as determined by the Hubble constant. However, the Hubble constant can change in the past and in the future, dependent on the observed value of density parameters (Ω). Ω on this graph corresponds to the ratio of the matter density to the critical density ( ).

Hubble's law

The metric expansion of space is a feature of many solutions to the Einstein field equations of general relativity, such as the Friedmann–Lemaître–Robertson–Walker metric and the Lemaître–Tolman–Bondi metric, where distance is measured using the Lorentz interval. This explains observations that indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us (see Hubble's law).

Cosmological constant and the Friedmann equations

The first general relativistic models predicted that a universe that was dynamical and contained ordinary gravitational matter would contract rather than expand. Einstein's first proposal for a solution to this problem involved adding a cosmological constant into his theories to balance out the contraction, in order to obtain a static universe solution. But in 1922 Alexander Friedmann derived a set of equations known as the Friedmann equations, showing that the universe might expand and presenting the expansion speed in this case.[33] The observations of Edwin Hubble in 1929 suggested that distant galaxies were all apparently moving away from us, so that many scientists came to accept that the universe was expanding.

Hubble's concerns over the rate of expansion

While the metric expansion of space appeared to be implied by Hubble's 1929 observations, Hubble disagreed with the expanding-universe interpretation of the data:

[...] if redshifts are not primarily due to velocity shift [...] the velocity-distance relation is linear; the distribution of the nebula is uniform; there is no evidence of expansion, no trace of curvature, no restriction of the time scale [...] and we find ourselves in the presence of one of the principles of nature that is still unknown to us today [...] whereas, if redshifts are velocity shifts which measure the rate of expansion, the expanding models are definitely inconsistent with the observations that have been made [...] expanding models are a forced interpretation of the observational results.

— E. Hubble, Ap. J., 84, 517, 1936[34]

[If the redshifts are a Doppler shift ...] the observations as they stand lead to the anomaly of a closed universe, curiously small and dense, and, it may be added, suspiciously young. On the other hand, if redshifts are not Doppler effects, these anomalies disappear and the region observed appears as a small, homogeneous, but insignificant portion of a universe extended indefinitely both in space and time.

— E. Hubble, Monthly Notices of the Royal Astronomical Society, 97, 506, 1937[35]

Hubble's skepticism about the universe being too small, dense, and young turned out to be based on an observational error. Later investigations appeared to show that Hubble had confused distant H II regions for Cepheid variables and the Cepheid variables themselves had been inappropriately lumped together with low-luminosity RR Lyrae stars causing calibration errors that led to a value of the Hubble Constant of approximately 500 km/s/Mpc instead of the true value of approximately 70 km/s/Mpc. The higher value meant that an expanding universe would have an age of 2 billion years (younger than the Age of the Earth) and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor, enough to force the universe into a peculiar closed geometry that also implied an impending Big Crunch that would occur on a similar timescale. After fixing these errors in the 1950s, the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe.[36]

However, recent measurements of the distances and velocities of faraway galaxies revealed a 9 percent discrepancy in the value of the Hubble constant, implying a universe that seems expanding too fast compared to previous measurements.[37] In 2001, Wendy Freedman determined space to expand at 72 kilometers per second per megaparsec - roughly 3.3 million light years - meaning that for every 3.3 million light years further away from the earth you are, the matter where you are, is moving away from earth 72 kilometers a second faster.[37] In the summer of 2016, another measurement reported a value of 73 for the constant, thereby contradicting 2013 measurements from the European Planck mission of slower expansion value of 67. The discrepancy opened new questions concerning the nature of dark energy, or of neutrinos.[37]

Inflation as an explanation for the expansion

Until the theoretical developments in the 1980s no one had an explanation for why this seemed to be the case, but with the development of models of cosmic inflation, the expansion of the universe became a general feature resulting from vacuum decay. Accordingly, the question "why is the universe expanding?" is now answered by understanding the details of the inflation decay process that occurred in the first 10−32 seconds of the existence of our universe.[38] During inflation, the metric changed exponentially, causing any volume of space that was smaller than an atom to grow to around 100 million light years across in a time scale similar to the time when inflation occurred (10−32 seconds).

Measuring distance in a metric space

 
The diagram depicts the expansion of the universe and the relative observer phenomenon. The blue galaxies have expanded further apart than the white galaxies. When choosing an arbitrary reference point such as the gold galaxy or the red galaxy, the increased distance to other galaxies the further away they are appear the same. This phenomenon of expansion indicates two factors: there is no centralized point in the universe, and that the Milky Way Galaxy is not the center of the universe. The appearance of centrality is due to an observer bias that is equivalent no matter what location an observer sits.
Main article: Comoving coordinates

In expanding space, distance is a dynamic quantity that changes with time. There are several different ways of defining distance in cosmology, known as distance measures, but a common method used amongst modern astronomers is comoving distance.

The metric only defines the distance between nearby (so-called "local") points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve (known as a "spacetime interval") connecting them. The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space. Comoving distance defines this connecting curve to be a curve of constant cosmological time. Operationally, comoving distances cannot be directly measured by a single Earth-bound observer. To determine the distance of distant objects, astronomers generally measure luminosity of standard candles, or the redshift factor 'z' of distant galaxies, and then convert these measurements into distances based on some particular model of spacetime, such as the Lambda-CDM model. It is, indeed, by making such observations that it was determined that there is no evidence for any 'slowing down' of the expansion in the current epoch.

Observational evidence

Theoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work. These workings have led to models in which the metric expansion of space is a likely feature of the universe. Chief among the underlying principles that result in models including metric expansion as a feature are:

  • the Cosmological Principle that demands that the universe looks the same way in all directions (isotropic) and has roughly the same smooth mixture of material (homogeneous).
  • the Copernican Principle that demands that no place in the universe is preferred (that is, the universe has no "starting point").

Scientists have tested carefully whether these assumptions are valid and borne out by observation. Observational cosmologists have discovered evidence – very strong in some cases – that supports these assumptions, and as a result, metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly, scientists have tested the properties of the universe and observation provides compelling confirmation.[39] Sources of this confidence and confirmation include:

  • Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion.[40] Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion. Further studies have since shown the expansion to be highly isotropic and homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.
  • In studies of large-scale structure of the cosmos taken from redshift surveys a so-called "End of Greatness" was discovered at the largest scales of the universe. Until these scales were surveyed, the universe appeared "lumpy" with clumps of galaxy clusters, superclusters and filaments that were anything but isotropic and homogeneous. This lumpiness disappears into a smooth distribution of galaxies at the largest scales.
  • The isotropic distribution across the sky of distant gamma-ray bursts and supernovae is another confirmation of the Cosmological Principle.
  • The Copernican Principle was not truly tested on a cosmological scale until measurements of the effects of the cosmic microwave background radiation on the dynamics of distant astrophysical systems were made. A group of astronomers at the European Southern Observatory noticed, by measuring the temperature of a distant intergalactic cloud in thermal equilibrium with the cosmic microwave background, that the radiation from the Big Bang was demonstrably warmer at earlier times.[41] Uniform cooling of the cosmic microwave background over billions of years is strong and direct observational evidence for metric expansion.

Taken together, these phenomena overwhelmingly support models that rely on space expanding through a change in metric. It was not until the discovery in the year 2000 of direct observational evidence for the changing temperature of the cosmic microwave background that more bizarre constructions could be ruled out. Until that time, it was based purely on an assumption that the universe did not behave as one with the Milky Way sitting at the middle of a fixed-metric with a universal explosion of galaxies in all directions (as seen in, for example, an early model proposed by Milne). Yet before this evidence, many rejected the Milne viewpoint based on the mediocrity principle.

More direct results of the expansion, such as change of redshift, distance, flux, angular position and the angular size of astronomical objects, have not been detected yet due to smallness of these effects. Change of the redshift or the flux could be observed by Square Kilometre Array or Extremely Large Telescope in the mid-2030s.[42]

See also

Notes

  1. ^ Although anything in a local reference frame cannot accelerate past the speed of light, this limitation does not restrict the expansion of the metric itself.

References

  1. ^ Overbye, Dennis (20 February 2017). "Cosmos Controversy: The Universe Is Expanding, but How Fast?". The New York Times. Retrieved 21 February 2017.
  2. ^ Radford, Tim (3 June 2016). "Universe is expanding up to 9% faster than we thought, say scientists". The Guardian. Retrieved 3 June 2016.
  3. ^ Slipher, V. M. (1913). "The Radial Velocity of the Andromeda Nebula". Lowell Observatory Bulletin. 1 (8): 56–57. Bibcode:1913LowOB...2...56S.
  4. ^ "Vesto Slipher – American astronomer".
  5. ^ Friedman, A. (1922). "Über die Krümmung des Raumes". Zeitschrift für Physik. 10 (1): 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902. translated in Friedmann, A. (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12): 1991–2000. Bibcode:1999GReGr..31.1991F. doi:10.1023/A:1026751225741. S2CID 122950995.
  6. ^ Who discovered Universe expansion?, Ian Steer, Nature 490, 176 (2012), accessed 4 December 2021
  7. ^ Lemaître, Georges (1927). "Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques" [A homogeneous universe of constant mass and increasing radius accounting for the radial speed of extra-galactic nebulae]. Annales de la Société Scientifique de Bruxelles. A47: 49–59. Bibcode:1927ASSB...47...49L.
  8. ^ "Astronomer sleuth solves mystery of Big Cosmos discovery". Space.com. 14 November 2011.
  9. ^ Baade W (1944) The resolution of Messier 32, NGC 205, and the central region of the Andromeda nebula. ApJ 100 137-146
  10. ^ Baade W (1956) The period-luminosity relation of the Cepheids. PASP 68 5-16
  11. ^ Allen, Nick. . The Cepheid Distance Scale: A History. Archived from the original on 10 December 2007. Retrieved 19 November 2011.
  12. ^ Trauger, J.T. (1994). ""The on-orbit performance of WFPC2"". Astrophysical Journal Letters. 435: L3. Bibcode:1994ApJ...435L...3T. doi:10.1086/187580.
  13. ^ Freedman, W.L.. A status report is given on the HST Hubble Constant Key Project. "The HST Key Project to Measure the Hubble Constant". Carnegie Observatories, 813 Santa Barbara St., Pasadena, CA 91101. https://www.stsci.edu/stsci/meetings/shst2/freedmanw.html
  14. ^ Riess, Adam G. (January 1995). ""Using Type IA supernova light curve shapes to measure the Hubble constant"". The Astrophysical Journal. 438: L17. arXiv:astro-ph/9410054. Bibcode:1995ApJ...438L..17R. doi:10.1086/187704. S2CID 118938423.
  15. ^ Spergel, D.N. (September 2003). "First-Year Wilkinson Microwave Anisotropy Probe (WMAP)1 Observations: Determination of Cosmological Parameters". The Astrophysical Journal Supplement Series. 148 (1): 175–194. arXiv:astro-ph/0302209. Bibcode:2003ApJS..148..175S. doi:10.1086/377226. S2CID 10794058.
  16. ^ Penrose, Roger (2016). Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press. doi:10.2307/j.ctvc775bn. ISBN 9781400880287. JSTOR j.ctvc775bn.
  17. ^ Riess, Adam G.; Macri, Lucas M.; Hoffmann, Samantha L.; Scolnic, Dan; Casertano, Stefano; Filippenko, Alexei V.; Tucker, Brad E.; Reid, Mark J.; Jones, David O.; Silverman, Jeffrey M.; Chornock, Ryan; Challis, Peter; Yuan, Wenlong; Brown, Peter J.; Foley, Ryan J. (2016). "A 2.4% Determination of the Local Value of the Hubble Constant". The Astrophysical Journal. 826 (1): 56. arXiv:1604.01424. Bibcode:2016ApJ...826...56R. doi:10.3847/0004-637X/826/1/56. S2CID 118630031.
  18. ^ Collaboration, Planck (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641: A6. arXiv:1807.06209. Bibcode:2020A&A...641A...6P. doi:10.1051/0004-6361/201833910. S2CID 119335614.
  19. ^ Overbye, Dennis (11 October 2003). "A 'Cosmic Jerk' That Reversed the universe". The New York Times.
  20. ^ The Nobel Prize in Physics 2011
  21. ^ Lerner, Louise (22 October 2018). "Gravitational waves could soon provide measure of universe's expansion". Phys.org. Retrieved 22 October 2018.
  22. ^ Chen, Hsin-Yu; Fishbach, Maya; Holz, Daniel E. (17 October 2018). "A two per cent Hubble constant measurement from standard sirens within five years". Nature. 562 (7728): 545–547. arXiv:1712.06531. Bibcode:2018Natur.562..545C. doi:10.1038/s41586-018-0606-0. PMID 30333628. S2CID 52987203.
  23. ^ Krauss, Lawrence M. (2012). A Universe from Nothing. Free Press. p. 82. ISBN 9781451624458.
  24. ^ What Do You Mean, The Universe Is Flat? (Part I), Scientific American, Davide Castelvecchi, July 25, 2011.
  25. ^ Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press. p. 73. ISBN 9780691019338.
  26. ^ Rothstein, Dave (23 April 2003). "What is the universe expanding into?". Ask an Astronomer. Retrieved 28 April 2017.
  27. ^ Pons, J. M.; Talavera, P. (2021). "On cosmological expansion and local physics". General Relativity and Gravitation. 53 (11): 105. arXiv:2011.01216. Bibcode:2021GReGr..53..105P. doi:10.1007/s10714-021-02874-4. S2CID 226236696.
  28. ^ Tamara M. Davis and Charles H. Lineweaver, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe. astro-ph/0310808
  29. ^ Alan B. Whiting (2004). "The Expansion of Space: Free Particle Motion and the Cosmological Redshift". The Observatory. 124: 174. arXiv:astro-ph/0404095. Bibcode:2004Obs...124..174W.
  30. ^ EF Bunn & DW Hogg (2009). "The kinematic origin of the cosmological redshift". American Journal of Physics. 77 (8): 688–694. arXiv:0808.1081. Bibcode:2009AmJPh..77..688B. doi:10.1119/1.3129103. S2CID 1365918.
  31. ^ Yu. V. Baryshev (2008). "Expanding Space: The Root of Conceptual Problems of the Cosmological Physics". Practical Cosmology. 2: 20–30. arXiv:0810.0153. Bibcode:2008pc2..conf...20B.
  32. ^ JA Peacock (2008). "A diatribe on expanding space". arXiv:0809.4573 [astro-ph].
  33. ^ Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377–386. (English translation in: Gen. Rel. Grav. 31 (1999), 1991–2000.)
  34. ^ Hubble, Edwin (1936). "Effects of Red Shifts on the Distribution of Nebulae". The Astrophysical Journal. 84 (11): 621–627. Bibcode:1936ApJ....84..517H. doi:10.1086/143782. PMC 1076828. PMID 16577738.
  35. ^ Hubble, Edwin (1937). "Red-shifts and the distribution of nebulæ". Monthly Notices of the Royal Astronomical Society. 97 (7): 506. Bibcode:1937MNRAS..97..506H. doi:10.1093/mnras/97.7.506.
  36. ^ Gingerich, Owen (1999). "A Brief History of Our View of the Universe". Publ. Astron. Soc. Pac. Astronomical Society of the Pacific. 111 (757): 254–257. Bibcode:1999PASP..111..254G. doi:10.1086/316324. JSTOR 10.1086/316324.
  37. ^ a b c Overbye, Dennis (20 February 2017). "Cosmos Controversy: The Universe Is Expanding, but How Fast?". The New York Times. ISSN 0362-4331. Retrieved 29 June 2017.
  38. ^ Interview with Alan Guth; THE INFLATIONARY UNIVERSE, [11.19.02] by Edge.org. [1]
  39. ^ Bennett, Charles L. (27 April 2006). "Cosmology from start to finish". Nature. 440 (7088): 1126–1131. Bibcode:2006Natur.440.1126B. doi:10.1038/nature04803. PMID 16641983. S2CID 4371349.
  40. ^ Hubble, Edwin, "A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae" (1929) Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173 (Full article, PDF)
  41. ^ Astronomers reported their measurement in a paper published in the December 2000 issue of Nature titled The microwave background temperature at the redshift of 2.33771, which can be read here [2]. A press release from the European Southern Observatory explains the findings to the public.
  42. ^ Direct detection of the cosmic expansion: the redshift drift and the flux drift

Printed references

  • Eddington, Arthur. The Expanding Universe: Astronomy's 'Great Debate', 1900-1931. Press Syndicate of the University of Cambridge, 1933.
  • Liddle, Andrew R. and David H. Lyth. Cosmological Inflation and Large-Scale Structure. Cambridge University Press, 2000.
  • Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the Big Bang", Scientific American, March 2005 (non-free content).
  • Mook, Delo E. and Thomas Vargish. Inside Relativity. Princeton University Press, 1991.

External links

 
Wikimedia Commons has media related to Expansion of the universe.
  • Swenson, Jim Answer to a question about the expanding universe 11 January 2009 at the Wayback Machine
  • Felder, Gary, "The Expanding universe".
  • NASA's WMAP team offers an "Explanation of the universal expansion" at a very elementary level
  • Hubble Tutorial from the University of Wisconsin Physics Department 9 June 2014 at the Wayback Machine
  • from the University of Winnipeg: an illustration, but no explanation
  • "Ant on a balloon" analogy to explain the expanding universe at "Ask an Astronomer". (The astronomer who provides this explanation is not specified.)

May 04, 2023
expansion, universe, expansion, universe, increase, distance, between, given, gravitationally, unbound, parts, observable, universe, with, time, intrinsic, expansion, whereby, scale, space, itself, changes, universe, does, expand, into, anything, does, require. The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time 1 It is an intrinsic expansion whereby the scale of space itself changes The universe does not expand into anything and does not require space to exist outside it This expansion involves neither space nor objects in space moving in a traditional sense but rather it is the metric which governs the size and geometry of spacetime itself that changes in scale As the spatial part of the universe s spacetime metric increases in scale objects become more distant from one another at ever increasing speeds To any observer in the universe it appears that all of space is expanding and that all but the nearest galaxies which are bound by gravity recede at speeds that are proportional to their distance from the observer While objects within space cannot travel faster than light this limitation does not apply to the effects of changes in the metric itself notes 1 Objects that recede beyond the cosmic event horizon will eventually become unobservable as no new light from them will be capable of overcoming the universe s expansion limiting the size of our observable universe As an effect of general relativity the expansion of the universe is different from the expansions and explosions seen in daily life It is a property of the universe as a whole and occurs throughout the universe rather than happening just to one part of the universe Therefore unlike other expansions and explosions it cannot be observed from outside of it it is believed that there is no outside to observe from Metric expansion is a key feature of Big Bang cosmology is modeled mathematically with the Friedmann Lemaitre Robertson Walker metric and is a generic property of the universe we inhabit However the model is valid only on large scales roughly the scale of galaxy clusters and above because gravity binds matter together strongly enough that metric expansion cannot be observed on a smaller scale at this time As such the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the universe given the matter density and average expansion rate According to inflation theory during the inflationary epoch about 10 32 of a second after the Big Bang the universe suddenly expanded and its volume increased by a factor of at least 1078 an expansion of distance by a factor of at least 1026 in each of the three dimensions This would be equivalent to expanding an object 1 nanometer 10 9 m about half the width of a molecule of DNA in length to one approximately 10 6 light years about 1017 m or 62 trillion miles long A much slower and gradual expansion of space continued after this until at around 9 8 billion years after the Big Bang 4 billion years ago it began to gradually expand more quickly and is still doing so Physicists have postulated the existence of dark energy appearing as a cosmological constant in the simplest gravitational models as a way to explain this late time acceleration According to the simplest extrapolation of the currently favored cosmological model the Lambda CDM model this acceleration becomes more dominant into the future In June 2016 NASA and ESA scientists reported that the universe was found to be expanding 5 to 9 faster than thought earlier based on studies using the Hubble Space Telescope 2 Contents 1 History 2 Cosmic inflation 3 Overview of metrics and comoving coordinates 3 1 Example Great Circle metric for Earth s surface 3 2 Metric tensors 3 3 Comoving coordinates 4 Understanding the expansion of the universe 4 1 Measurement of expansion and change of rate of expansion 4 2 Measuring distances in expanding space 4 3 Topology of expanding space 4 4 Density of universe during expansion 4 5 Effects of expansion on small scales 4 6 Metric expansion and speed of light 4 7 Scale factor 4 8 Other conceptual models of expansion 5 Theoretical basis and first evidence 5 1 Hubble s law 5 2 Cosmological constant and the Friedmann equations 5 3 Hubble s concerns over the rate of expansion 5 4 Inflation as an explanation for the expansion 5 5 Measuring distance in a metric space 6 Observational evidence 7 See also 8 Notes 9 References 10 Printed references 11 External linksHistory EditIn 1912 Vesto Slipher discovered that light from remote galaxies was redshifted 3 4 which was later interpreted as galaxies receding from the Earth In 1922 Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding 5 Swedish astronomer Knut Lundmark was the first person to find observational evidence for expansion in 1924 According to Ian Steer of the NASA IPAC Extragalactic Database of Galaxy Distances Lundmark s extragalactic distance estimates were far more accurate than Hubble s consistent with an expansion rate Hubble constant that was within 1 of the best measurements today 6 In 1927 Georges Lemaitre independently reached a similar conclusion to Friedmann on a theoretical basis and also presented observational evidence for a linear relationship between distance to galaxies and their recessional velocity 7 Edwin Hubble observationally confirmed Lundmark s and Lemaitre s findings in 1929 8 Assuming the cosmological principle these findings would imply that all galaxies are moving away from each other Astronomer Walter Baade recalculated the size of the known universe in the 1940s doubling the previous calculation made by Hubble in 1929 9 10 11 He announced this finding to considerable astonishment at the 1952 meeting of the International Astronomical Union in Rome For most of the second half of the 20th century the value of the Hubble constant was estimated to be between 50 and 90 km s Mpc Based on large quantities of experimental observation and theoretical work the scientific consensus is that space itself is expanding and that it expanded very rapidly within the first fraction of a second after the Big Bang approximately 13 8 billion years ago This kind of expansion is known as metric expansion In mathematics and physics a metric means a measure of distance and the term implies that the sense of distance within the universe is itself changing On 13 January 1994 NASA formally announced a completion of its repairs on the main mirror of the Hubble Space Telescope allowing for sharper images and consequently more accurate analyses of its observations 12 Briefly after the repairs were made Wendy Freedman s 1994 Key Project analyzed the recession velocity of M100 from the core of the Virgo cluster offering a Hubble constant measurement of 80 17 km s 1 Mpc 1 Mega Parsec 13 Later the same year Adam Riess et al utilized an empirical method of visual band light shape curves to more finely estimate the luminosity of Type Ia supernova This further minimized the systemic measurement errors of the Hubble constant to 67 7 km s 1 Mpc 1 Reiss s measurements on the recession velocity of the nearby Virgo cluster more closely agree with subsequent and independent analyses of Cepheid variable calibrations of 1a supernovae which estimates a Hubble Constant of 73 7km s 1 Mpc 1 14 Within the next decade in 2003 David Spergel s analysis of the Cosmic microwave background during the first year observations of the Wilkinson Microwave Anisotropy Probe satellite WMAP further agreed with the estimated expansion rates for local galaxies 72 5 km s 1 Mpc 1 15 Cosmic inflation EditMain articles inflation cosmology and inflaton The modern explanation for the metric expansion of space was proposed by physicist Alan Guth in 1979 while investigating the problem of why no magnetic monopoles are seen today Guth found in his investigation that if the universe contained a field that has a positive energy false vacuum state then according to general relativity it would generate an exponential expansion of space It was very quickly realized that such an expansion would resolve many other long standing problems These problems arise from the observation that to look as it does today the universe would have to have started from very finely tuned or special initial conditions at the Big Bang Inflation theory largely resolves these problems as well thus making a universe like ours much more likely in the context of Big Bang theory According to Roger Penrose inflation does not solve the main problem it was supposed to solve namely the incredibly low entropy with unlikeliness of the state on the order of 1 1010128 of the early Universe contained in the gravitational conformal degrees of freedom in contrast to fields degrees of freedom such like the cosmic microwave background whose smoothness can be explained by inflation Thus he puts forward his scenario of the evolution of the Universe conformal cyclic cosmology 16 No field responsible for cosmic inflation has been discovered However such a field if found in the future would be scalar The first similar scalar field proven to exist was only discovered in 2012 2013 and is still being researched So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered citation needed The proposed field and its quanta the subatomic particles related to it have been named inflaton If this field did not exist scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred and is still occurring much more slowly today Overview of metrics and comoving coordinates EditMain articles Metric mathematics and tensor To understand the metric expansion of the universe it is helpful to discuss briefly what a metric is and how metric expansion works A metric defines the concept of distance by stating in mathematical terms how distances between two nearby points in space are measured in terms of the coordinate system Coordinate systems locate points in a space of whatever number of dimensions by assigning unique positions on a grid known as coordinates to each point Latitude and longitude and x y graphs are common examples of coordinates A metric is a formula that describes how a number known as distance is to be measured between two points It may seem obvious that distance is measured by a straight line but in many cases it is not For example long haul aircraft travel along a curve known as a great circle and not a straight line because that is a better metric for air travel A straight line would go through the earth Another example is planning a car journey where one might want the shortest journey in terms of travel time in that case a straight line is a poor choice of metric because the shortest distance by road is not normally a straight line and even the path nearest to a straight line will not necessarily be the quickest A final example is the internet where even for nearby towns the quickest route for data can be via major connections that go across the country and back again In this case the metric used will be the shortest time that data takes to travel between two points on the network In cosmology we cannot use a ruler to measure metric expansion because our ruler s internal forces easily overcome the extremely slow expansion of space leaving the ruler intact Also any objects on or near earth that we might measure are being held together or pushed apart by several forces that are far larger in their effects So even if we could measure the tiny expansion that is still happening we would not notice the change on a small scale or in everyday life On a large intergalactic scale we can use other tests of distance and these do show that space is expanding even if a ruler on earth could not measure it The metric expansion of space is described using the mathematics of metric tensors The coordinate system we use is called comoving coordinates a type of coordinate system that takes account of time as well as space and the speed of light and allows us to incorporate the effects of both general and special relativity Example Great Circle metric for Earth s surface Edit For example consider the measurement of distance between two places on the surface of the Earth This is a simple familiar example of spherical geometry Because the surface of the Earth is two dimensional points on the surface of the Earth can be specified by two coordinates for example the latitude and longitude Specification of a metric requires that one first specify the coordinates used In our simple example of the surface of the Earth we could choose any kind of coordinate system we wish for example latitude and longitude or X Y Z Cartesian coordinates Once we have chosen a specific coordinate system the numerical values of the coordinates of any two points are uniquely determined and based upon the properties of the space being discussed the appropriate metric is mathematically established too On the curved surface of the Earth we can see this effect in long haul airline flights where the distance between two points is measured based upon a great circle rather than the straight line one might plot on a two dimensional map of the Earth s surface In general such shortest distance paths are called geodesics In Euclidean geometry the geodesic is a straight line while in non Euclidean geometry such as on the Earth s surface this is not the case Indeed even the shortest distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth The difference between the straight line path and the shortest distance great circle path is due to the curvature of the Earth s surface While there is always an effect due to this curvature at short distances the effect is small enough to be unnoticeable On plane maps great circles of the Earth are mostly not shown as straight lines Indeed there is a seldom used map projection namely the gnomonic projection where all great circles are shown as straight lines but in this projection the distance scale varies very much in different areas There is no map projection in which the distance between any two points on Earth measured along the great circle geodesics is directly proportional to their distance on the map such accuracy is possible only with a globe Metric tensors Edit In differential geometry the backbone mathematics for general relativity a metric tensor can be defined that precisely characterizes the space being described by explaining the way distances should be measured in every possible direction General relativity necessarily invokes a metric in four dimensions one of time three of space because in general different reference frames will experience different intervals of time and space depending on the inertial frame This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated A metric expansion occurs when the metric tensor changes with time and specifically whenever the spatial part of the metric gets larger as time goes forward This kind of expansion is different from all kinds of expansions and explosions commonly seen in nature in no small part because times and distances are not the same in all reference frames but are instead subject to change A useful visualization is rather than imagining objects in a fixed space moving apart into emptiness instead imagine space itself growing between all objects without any acceleration or movement of the objects themselves The space between objects shrinks or grows as the various geodesics converge or diverge Because this expansion is caused by relative changes in the distance defining metric this expansion and the resultant movement apart of objects is not restricted by the speed of light upper bound of special relativity Two reference frames that are globally separated can be moving apart faster than light without violating special relativity although whenever two reference frames diverge from each other faster than the speed of light there will be observable effects associated with such situations including the existence of various cosmological horizons Theory and observations suggest that very early in the history of the universe there was an inflationary phase where the metric changed very rapidly and that the remaining time dependence of this metric is what we observe as the so called Hubble expansion the moving apart of all gravitationally unbound objects in the universe The expanding universe is therefore a fundamental feature of the universe we inhabit a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory Comoving coordinates Edit Main article Comoving coordinates In expanding space proper distances are dynamical quantities that change with time An easy way to correct for this is to use comoving coordinates which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion In comoving coordinates the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation Any time evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations in addition to any other effects that may be operating gravity dark energy or curvature for example Cosmological simulations that run through significant fractions of the universe s history therefore must include such effects in order to make applicable predictions for observational cosmology Understanding the expansion of the universe EditMeasurement of expansion and change of rate of expansion Edit When an object is receding its light gets stretched redshifted When the object is approaching its light gets compressed blueshifted In principle the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points waiting a certain time and then measuring the distance again but in practice standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans The expansion of space is measured indirectly The theory of relativity predicts phenomena associated with the expansion notably the redshift versus distance relationship known as Hubble s Law functional forms for cosmological distance measurements that differ from what would be expected if space were not expanding and an observable change in the matter and energy density of the universe seen at different lookback times The first measurement of the expansion of space came with Hubble s realization of the velocity vs redshift relation Most recently by comparing the apparent brightness of distant standard candles to the redshift of their host galaxies the expansion rate of the universe has been measured to be H0 73 24 1 74 km s Mpc 17 This means that for every million parsecs of distance from the observer the light received from that distance is cosmologically redshifted by about 73 kilometres per second 160 000 mph On the other hand by assuming a cosmological model e g Lambda CDM model one can infer the Hubble constant from the size of the largest fluctuations seen in the Cosmic Microwave Background A higher Hubble constant would imply a smaller characteristic size of CMB fluctuations and vice versa The Planck collaboration measure the expansion rate this way and determine H0 67 4 0 5 km s Mpc 18 There is a disagreement between the two measurements the distance ladder being model independent and the CMB measurement depending on the fitted model which hints at new physics beyond our standard cosmological models The Hubble parameter is not thought to be constant through time There are dynamical forces acting on the particles in the universe that affect the expansion rate It was earlier expected that the Hubble parameter would be decreasing as time went on due to the influence of gravitational interactions in the universe and thus there is an additional observable quantity in the universe called the deceleration parameter which cosmologists expected to be directly related to the matter density of the universe Surprisingly the deceleration parameter was measured by two different groups to be less than zero actually consistent with 1 which implied that today the Hubble parameter is converging to a constant value as time goes on Some cosmologists have whimsically called the effect associated with the accelerating universe the cosmic jerk 19 The 2011 Nobel Prize in Physics was given for the discovery of this phenomenon 20 In October 2018 scientists presented a new third way two earlier methods one based on redshifts and another on the cosmic distance ladder gave results that do not agree using information from gravitational wave events especially those involving the merger of neutron stars like GW170817 of determining the Hubble Constant essential in establishing the rate of expansion of the universe 21 22 Measuring distances in expanding space Edit This article has multiple issues Please help improve it or discuss these issues on the talk page Learn how and when to remove these template messages This section is written like a personal reflection personal essay or argumentative essay that states a Wikipedia editor s personal feelings or presents an original argument about a topic Please help improve it by rewriting it in an encyclopedic style August 2015 Learn how and when to remove this template message This section needs additional citations for verification Please help improve this article by adding citations to reliable sources in this section Unsourced material may be challenged and removed Find sources Expansion of the universe news newspapers books scholar JSTOR May 2021 Learn how and when to remove this template message Learn how and when to remove this template message Two views of an isometric embedding of part of the visible universe over most of its history showing how a light ray red line can travel an effective distance of 28 billion light years orange line in just 13 billion years of cosmological time Mathematical details At cosmological scales the present universe conforms to Euclidean space what cosmologists describe as geometrically flat to within experimental error 23 Consequently the rules of Euclidean geometry associated with Euclid s fifth postulate hold in the present universe in 3D space It is however possible that the geometry of past 3D space could have been highly curved The curvature of space is often modeled using a non zero Riemann curvature tensor in Curvature of Riemannian manifolds Euclidean geometrically flat space has a Riemann curvature tensor of zero Geometrically flat space has 3 dimensions and is consistent with Euclidean space However spacetime on the other hand is 4 dimensions it is not flat according to Einsten s general theory of relativity Einstein s theory postulates that matter and energy curve spacetime and there are enough matter and energy lying around to provide for curvature 24 In part to accommodate such different geometries the expansion of the universe is inherently general relativistic It cannot be modeled with special relativity alone though such models exist they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe The images to the right show two views of spacetime diagrams that show the large scale geometry of the universe according to the LCDM cosmological model Two of the dimensions of space are omitted leaving one dimension of space the dimension that grows as the cone gets larger and one of time the dimension that proceeds up the cone s surface The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the Big Bang while the wide end is a cosmological time of 18 billion years where one can see the beginning of the accelerating expansion as a splaying outward of the spacetime a feature that eventually dominates in this model The purple grid lines mark off cosmological time at intervals of one billion years from the Big Bang The cyan grid lines mark off comoving distance at intervals of one billion light years in the present era less in the past and more in the future Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely for illustrative purposes a flat universe does not curl back onto itself A similar effect can be seen in the tubular shape of the pseudosphere The brown line on the diagram is the worldline of Earth or more precisely its location in space even before it was formed The yellow line is the worldline of the most distant known quasar The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching Earth at the present day The orange line shows the present day distance between the quasar and Earth about 28 billion light years which is a larger distance than the age of the universe multiplied by the speed of light ct According to the equivalence principle of general relativity the rules of special relativity are locally valid in small regions of spacetime that are approximately flat In particular light always travels locally at the speed c in the diagram this means according to the convention of constructing spacetime diagrams that light beams always make an angle of 45 with the local grid lines It does not follow however that light travels a distance ct in a time t as the red worldline illustrates While it always moves locally at c its time in transit about 13 billion years is not related to the distance traveled in any simple way since the universe expands as the light beam traverses space and time The distance traveled is thus inherently ambiguous because of the changing scale of the universe Nevertheless there are two distances that appear to be physically meaningful the distance between Earth and the quasar when the light was emitted and the distance between them in the present era taking a slice of the cone along the dimension defined as the spatial dimension The former distance is about 4 billion light years much smaller than ct whereas the latter distance shown by the orange line is about 28 billion light years much larger than ct In other words if space were not expanding today it would take 28 billion years for light to travel between Earth and the quasar while if the expansion had stopped at the earlier time it would have taken only 4 billion years The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away In fact the light emitted towards Earth was actually moving away from Earth when it was first emitted the metric distance to Earth increased with cosmological time for the first few billion years of its travel time also indicating that the expansion of space between Earth and the quasar at the early time was faster than the speed of light None of this behavior originates from a special property of metric expansion but rather from local principles of special relativity integrated over a curved surface Topology of expanding space Edit A graphical representation of the expansion of the universe from the Big Bang to the present day with the inflationary epoch represented as the dramatic expansion of the metric seen on the left This visualization can be confusing because it appears as if the universe is expanding into a pre existing empty space over time Instead the expansion created and continues to create all of known space and time Over time the space that makes up the universe is expanding The words space and universe sometimes used interchangeably have distinct meanings in this context Here space is a mathematical concept that stands for the three dimensional manifold into which our respective positions are embedded while universe refers to everything that exists including the matter and energy in space the extra dimensions that may be wrapped up in various strings and the time through which various events take place The expansion of space is in reference to this 3 D manifold only that is the description involves no structures such as extra dimensions or an exterior universe 25 The ultimate topology of space is a posteriori something that in principle must be observed as there are no constraints that can simply be reasoned out in other words there can not be any a priori constraints on how the space in which we live is connected or whether it wraps around on itself as a compact space Though certain cosmological models such as Godel s universe even permit bizarre worldlines that intersect with themselves ultimately the question as to whether we are in something like a Pac Man universe where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon or a planet like the Earth is an observational question that is constrained as measurable or non measurable by the universe s global geometry At present observations are consistent with the universe being infinite in extent and simply connected though we are limited in distinguishing between simple and more complicated proposals by cosmological horizons The universe could be infinite in extent or it could be finite but the evidence that leads to the inflationary model of the early universe also implies that the total universe is much larger than the observable universe and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe if they exist are still allowed For all intents and purposes it is safe to assume that the universe is infinite in spatial extent without edge or strange connectedness 26 Regardless of the overall shape of the universe the question of what the universe is expanding into is one that does not require an answer according to the theories that describe the expansion the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on This only implies the simple observational consequences associated with the metric expansion explored below No outside or embedding in hyperspace is required for an expansion to occur The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect There is no reason to believe there is anything outside of the expanding universe into which the universe expands Even if the overall spatial extent is infinite and thus the universe cannot get any larger we still say that space is expanding because locally the characteristic distance between objects is increasing As an infinite space grows it remains infinite Density of universe during expansion Edit Despite being extremely dense when very young and during part of its early expansion far denser than is usually required to form a black hole the universe did not re collapse into a black hole This is because commonly used calculations for gravitational collapse are usually based upon objects of relatively constant size such as stars and do not apply to rapidly expanding space such as the Big Bang Effects of expansion on small scales Edit The expansion of space is sometimes described as a force that acts to push objects apart Though this is an accurate description of the effect of the cosmological constant it is not an accurate picture of the phenomenon of expansion in general 27 Animation of an expanding raisin bread model As the bread doubles in width depth and length the distances between raisins also double In addition to slowing the overall expansion gravity causes local clumping of matter into stars and galaxies Once objects are formed and bound by gravity they drop out of the expansion and do not subsequently expand under the influence of the cosmological metric there being no force compelling them to do so There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum the former is simply a large scale extrapolation of the latter Once objects are bound by gravity they no longer recede from each other Thus the Andromeda galaxy which is bound to the Milky Way galaxy is actually falling towards us and is not expanding away Within the Local Group the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place Once one goes beyond the Local Group the inertial expansion is measurable though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the Hubble Flow and end up as bound non expanding objects up to the scales of superclusters of galaxies We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled Currently the Local Group is being gravitationally pulled towards either the Shapley Supercluster or the Great Attractor with which if dark energy were not acting we would eventually merge and no longer see expand away from us after such a time A consequence of metric expansion being due to inertial motion is that a uniform local explosion of matter into a vacuum can be locally described by the FLRW geometry the same geometry that describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe which ignores the effects of gravity In particular general relativity predicts that light will move at the speed c with respect to the local motion of the exploding matter a phenomenon analogous to frame dragging The situation changes somewhat with the introduction of dark energy or a cosmological constant A cosmological constant due to a vacuum energy density has the effect of adding a repulsive force between objects that is proportional not inversely proportional to distance Unlike inertia it actively pulls on objects that have clumped together under the influence of gravity and even on individual atoms However this does not cause the objects to grow steadily or to disintegrate unless they are very weakly bound they will simply settle into an equilibrium state that is slightly undetectably larger than it would otherwise have been As the universe expands and the matter in it thins the gravitational attraction decreases since it is proportional to the density while the cosmological repulsion increases Thus the ultimate fate of the LCDM universe is a near vacuum expanding at an ever increasing rate under the influence of the cosmological constant However the only locally visible effect of the accelerating expansion is the disappearance by runaway redshift of distant galaxies Gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time It is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby Virgo Cluster However galaxies lying farther away from this will recede away at ever increasing speed and be redshifted out of our range of visibility Metric expansion and speed of light Edit At the end of the early universe s inflationary period all the matter and energy in the universe was set on an inertial trajectory consistent with the equivalence principle and Einstein s general theory of relativity and this is when the precise and regular form of the universe s expansion had its origin that is matter in the universe is separating because it was separating in the past due to the inflaton field citation needed While special relativity prohibits objects from moving faster than light with respect to a local reference frame where spacetime can be treated as flat and unchanging it does not apply to situations where spacetime curvature or evolution in time become important These situations are described by general relativity which allows the separation between two distant objects to increase faster than the speed of light although the definition of distance here is somewhat different from that used in an inertial frame The definition of distance used here is the summation or integration of local comoving distances all done at constant local proper time For example galaxies that are farther than the Hubble radius approximately 4 5 gigaparsecs or 14 7 billion light years away from us have a recession speed that is faster than the speed of light Visibility of these objects depends on the exact expansion history of the universe Light that is emitted today from galaxies beyond the more distant cosmological event horizon about 5 gigaparsecs or 16 billion light years will never reach us although we can still see the light that these galaxies emitted in the past Because of the high rate of expansion it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe These details are a frequent source of confusion among amateurs and even professional physicists 28 Due to the non intuitive nature of the subject and what has been described by some as careless choices of wording certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within the fields of education and communication of scientific concepts 29 30 31 32 Scale factor Edit At a fundamental level the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below This feature of the universe can be characterized by a single parameter that is called the scale factor which is a function of time and a single value for all of space at any instant if the scale factor were a function of space this would violate the cosmological principle By convention the scale factor is set to be unity at the present time and because the universe is expanding is smaller in the past and larger in the future Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero our current understanding of cosmology sets this time at 13 787 0 020 billion years ago If the universe continues to expand forever the scale factor will approach infinity in the future In principle there is no reason that the expansion of the universe must be monotonic and there are models where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion Other conceptual models of expansion Edit The expansion of space is often illustrated with conceptual models that show only the size of space at a particular time leaving the dimension of time implicit In the ant on a rubber rope model one imagines an ant idealized as pointlike crawling at a constant speed on a perfectly elastic rope that is constantly stretching If we stretch the rope in accordance with the LCDM scale factor and think of the ant s speed as the speed of light then this analogy is numerically accurate the ant s position over time will match the path of the red line on the embedding diagram above In the rubber sheet model one replaces the rope with a flat two dimensional rubber sheet that expands uniformly in all directions The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet In the balloon model the flat sheet is replaced by a spherical balloon that is inflated from an initial size of zero representing the big bang A balloon has positive Gaussian curvature while observations suggest that the real universe is spatially flat but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon In fact points off the surface of the balloon have no meaning even if they were occupied by the balloon at an earlier time In the raisin bread model one imagines a loaf of raisin bread expanding in the oven The loaf space expands as a whole but the raisins gravitationally bound objects do not expand they merely grow farther away from each other Theoretical basis and first evidence Edit The expansion of the universe proceeds in all directions as determined by the Hubble constant However the Hubble constant can change in the past and in the future dependent on the observed value of density parameters W W on this graph corresponds to the ratio of the matter density to the critical density W m displaystyle Omega m Hubble s law Edit The metric expansion of space is a feature of many solutions to the Einstein field equations of general relativity such as the Friedmann Lemaitre Robertson Walker metric and the Lemaitre Tolman Bondi metric where distance is measured using the Lorentz interval This explains observations that indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us see Hubble s law Cosmological constant and the Friedmann equations Edit The first general relativistic models predicted that a universe that was dynamical and contained ordinary gravitational matter would contract rather than expand Einstein s first proposal for a solution to this problem involved adding a cosmological constant into his theories to balance out the contraction in order to obtain a static universe solution But in 1922 Alexander Friedmann derived a set of equations known as the Friedmann equations showing that the universe might expand and presenting the expansion speed in this case 33 The observations of Edwin Hubble in 1929 suggested that distant galaxies were all apparently moving away from us so that many scientists came to accept that the universe was expanding Hubble s concerns over the rate of expansion Edit While the metric expansion of space appeared to be implied by Hubble s 1929 observations Hubble disagreed with the expanding universe interpretation of the data if redshifts are not primarily due to velocity shift the velocity distance relation is linear the distribution of the nebula is uniform there is no evidence of expansion no trace of curvature no restriction of the time scale and we find ourselves in the presence of one of the principles of nature that is still unknown to us today whereas if redshifts are velocity shifts which measure the rate of expansion the expanding models are definitely inconsistent with the observations that have been made expanding models are a forced interpretation of the observational results E Hubble Ap J 84 517 1936 34 If the redshifts are a Doppler shift the observations as they stand lead to the anomaly of a closed universe curiously small and dense and it may be added suspiciously young On the other hand if redshifts are not Doppler effects these anomalies disappear and the region observed appears as a small homogeneous but insignificant portion of a universe extended indefinitely both in space and time E Hubble Monthly Notices of the Royal Astronomical Society 97 506 1937 35 Hubble s skepticism about the universe being too small dense and young turned out to be based on an observational error Later investigations appeared to show that Hubble had confused distant H II regions for Cepheid variables and the Cepheid variables themselves had been inappropriately lumped together with low luminosity RR Lyrae stars causing calibration errors that led to a value of the Hubble Constant of approximately 500 km s Mpc instead of the true value of approximately 70 km s Mpc The higher value meant that an expanding universe would have an age of 2 billion years younger than the Age of the Earth and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor enough to force the universe into a peculiar closed geometry that also implied an impending Big Crunch that would occur on a similar timescale After fixing these errors in the 1950s the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe 36 However recent measurements of the distances and velocities of faraway galaxies revealed a 9 percent discrepancy in the value of the Hubble constant implying a universe that seems expanding too fast compared to previous measurements 37 In 2001 Wendy Freedman determined space to expand at 72 kilometers per second per megaparsec roughly 3 3 million light years meaning that for every 3 3 million light years further away from the earth you are the matter where you are is moving away from earth 72 kilometers a second faster 37 In the summer of 2016 another measurement reported a value of 73 for the constant thereby contradicting 2013 measurements from the European Planck mission of slower expansion value of 67 The discrepancy opened new questions concerning the nature of dark energy or of neutrinos 37 Inflation as an explanation for the expansion Edit Until the theoretical developments in the 1980s no one had an explanation for why this seemed to be the case but with the development of models of cosmic inflation the expansion of the universe became a general feature resulting from vacuum decay Accordingly the question why is the universe expanding is now answered by understanding the details of the inflation decay process that occurred in the first 10 32 seconds of the existence of our universe 38 During inflation the metric changed exponentially causing any volume of space that was smaller than an atom to grow to around 100 million light years across in a time scale similar to the time when inflation occurred 10 32 seconds Measuring distance in a metric space Edit The diagram depicts the expansion of the universe and the relative observer phenomenon The blue galaxies have expanded further apart than the white galaxies When choosing an arbitrary reference point such as the gold galaxy or the red galaxy the increased distance to other galaxies the further away they are appear the same This phenomenon of expansion indicates two factors there is no centralized point in the universe and that the Milky Way Galaxy is not the center of the universe The appearance of centrality is due to an observer bias that is equivalent no matter what location an observer sits Main article Comoving coordinates In expanding space distance is a dynamic quantity that changes with time There are several different ways of defining distance in cosmology known as distance measures but a common method used amongst modern astronomers is comoving distance The metric only defines the distance between nearby so called local points In order to define the distance between arbitrarily distant points one must specify both the points and a specific curve known as a spacetime interval connecting them The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space Comoving distance defines this connecting curve to be a curve of constant cosmological time Operationally comoving distances cannot be directly measured by a single Earth bound observer To determine the distance of distant objects astronomers generally measure luminosity of standard candles or the redshift factor z of distant galaxies and then convert these measurements into distances based on some particular model of spacetime such as the Lambda CDM model It is indeed by making such observations that it was determined that there is no evidence for any slowing down of the expansion in the current epoch Observational evidence EditTheoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work These workings have led to models in which the metric expansion of space is a likely feature of the universe Chief among the underlying principles that result in models including metric expansion as a feature are the Cosmological Principle that demands that the universe looks the same way in all directions isotropic and has roughly the same smooth mixture of material homogeneous the Copernican Principle that demands that no place in the universe is preferred that is the universe has no starting point Scientists have tested carefully whether these assumptions are valid and borne out by observation Observational cosmologists have discovered evidence very strong in some cases that supports these assumptions and as a result metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly scientists have tested the properties of the universe and observation provides compelling confirmation 39 Sources of this confidence and confirmation include Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us as predicted by a universal expansion 40 Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space he showed that all objects are moving away from us and that their speed is proportional to their distance a feature of metric expansion Further studies have since shown the expansion to be highly isotropic and homogeneous that is it does not seem to have a special point as a center but appears universal and independent of any fixed central point In studies of large scale structure of the cosmos taken from redshift surveys a so called End of Greatness was discovered at the largest scales of the universe Until these scales were surveyed the universe appeared lumpy with clumps of galaxy clusters superclusters and filaments that were anything but isotropic and homogeneous This lumpiness disappears into a smooth distribution of galaxies at the largest scales The isotropic distribution across the sky of distant gamma ray bursts and supernovae is another confirmation of the Cosmological Principle The Copernican Principle was not truly tested on a cosmological scale until measurements of the effects of the cosmic microwave background radiation on the dynamics of distant astrophysical systems were made A group of astronomers at the European Southern Observatory noticed by measuring the temperature of a distant intergalactic cloud in thermal equilibrium with the cosmic microwave background that the radiation from the Big Bang was demonstrably warmer at earlier times 41 Uniform cooling of the cosmic microwave background over billions of years is strong and direct observational evidence for metric expansion Taken together these phenomena overwhelmingly support models that rely on space expanding through a change in metric It was not until the discovery in the year 2000 of direct observational evidence for the changing temperature of the cosmic microwave background that more bizarre constructions could be ruled out Until that time it was based purely on an assumption that the universe did not behave as one with the Milky Way sitting at the middle of a fixed metric with a universal explosion of galaxies in all directions as seen in for example an early model proposed by Milne Yet before this evidence many rejected the Milne viewpoint based on the mediocrity principle More direct results of the expansion such as change of redshift distance flux angular position and the angular size of astronomical objects have not been detected yet due to smallness of these effects Change of the redshift or the flux could be observed by Square Kilometre Array or Extremely Large Telescope in the mid 2030s 42 See also EditComoving and proper distancesNotes Edit Although anything in a local reference frame cannot accelerate past the speed of light this limitation does not restrict the expansion of the metric itself References Edit Overbye Dennis 20 February 2017 Cosmos Controversy The Universe Is Expanding but How Fast The New York Times Retrieved 21 February 2017 Radford Tim 3 June 2016 Universe is expanding up to 9 faster than we thought say scientists The Guardian Retrieved 3 June 2016 Slipher V M 1913 The Radial Velocity of the Andromeda Nebula Lowell Observatory Bulletin 1 8 56 57 Bibcode 1913LowOB 2 56S Vesto Slipher American astronomer Friedman A 1922 Uber die Krummung des Raumes Zeitschrift fur Physik 10 1 377 386 Bibcode 1922ZPhy 10 377F doi 10 1007 BF01332580 S2CID 125190902 translated in Friedmann A 1999 On the Curvature of Space General Relativity and Gravitation 31 12 1991 2000 Bibcode 1999GReGr 31 1991F doi 10 1023 A 1026751225741 S2CID 122950995 Who discovered Universe expansion Ian Steer Nature 490 176 2012 accessed 4 December 2021 Lemaitre Georges 1927 Un Univers homogene de masse constante et de rayon croissant rendant compte de la vitesse radiale des nebuleuses extra galactiques A homogeneous universe of constant mass and increasing radius accounting for the radial speed of extra galactic nebulae Annales de la Societe Scientifique de Bruxelles A47 49 59 Bibcode 1927ASSB 47 49L Astronomer sleuth solves mystery of Big Cosmos discovery Space com 14 November 2011 Baade W 1944 The resolution of Messier 32 NGC 205 and the central region of the Andromeda nebula ApJ 100 137 146 Baade W 1956 The period luminosity relation of the Cepheids PASP 68 5 16 Allen Nick Section 2 The Great Debate and the Great Mistake Shapley Hubble Baade The Cepheid Distance Scale A History Archived from the original on 10 December 2007 Retrieved 19 November 2011 Trauger J T 1994 The on orbit performance of WFPC2 Astrophysical Journal Letters 435 L3 Bibcode 1994ApJ 435L 3T doi 10 1086 187580 Freedman W L A status report is given on the HST Hubble Constant Key Project The HST Key Project to Measure the Hubble Constant Carnegie Observatories 813 Santa Barbara St Pasadena CA 91101 https www stsci edu stsci meetings shst2 freedmanw html Riess Adam G January 1995 Using Type IA supernova light curve shapes to measure the Hubble constant The Astrophysical Journal 438 L17 arXiv astro ph 9410054 Bibcode 1995ApJ 438L 17R doi 10 1086 187704 S2CID 118938423 Spergel D N September 2003 First Year Wilkinson Microwave Anisotropy Probe WMAP 1 Observations Determination of Cosmological Parameters The Astrophysical Journal Supplement Series 148 1 175 194 arXiv astro ph 0302209 Bibcode 2003ApJS 148 175S doi 10 1086 377226 S2CID 10794058 Penrose Roger 2016 Fashion Faith and Fantasy in the New Physics of the Universe Princeton University Press doi 10 2307 j ctvc775bn ISBN 9781400880287 JSTOR j ctvc775bn Riess Adam G Macri Lucas M Hoffmann Samantha L Scolnic Dan Casertano Stefano Filippenko Alexei V Tucker Brad E Reid Mark J Jones David O Silverman Jeffrey M Chornock Ryan Challis Peter Yuan Wenlong Brown Peter J Foley Ryan J 2016 A 2 4 Determination of the Local Value of the Hubble Constant The Astrophysical Journal 826 1 56 arXiv 1604 01424 Bibcode 2016ApJ 826 56R doi 10 3847 0004 637X 826 1 56 S2CID 118630031 Collaboration Planck 2020 Planck 2018 results VI Cosmological parameters Astronomy amp Astrophysics 641 A6 arXiv 1807 06209 Bibcode 2020A amp A 641A 6P doi 10 1051 0004 6361 201833910 S2CID 119335614 Overbye Dennis 11 October 2003 A Cosmic Jerk That Reversed the universe The New York Times The Nobel Prize in Physics 2011 Lerner Louise 22 October 2018 Gravitational waves could soon provide measure of universe s expansion Phys org Retrieved 22 October 2018 Chen Hsin Yu Fishbach Maya Holz Daniel E 17 October 2018 A two per cent Hubble constant measurement from standard sirens within five years Nature 562 7728 545 547 arXiv 1712 06531 Bibcode 2018Natur 562 545C doi 10 1038 s41586 018 0606 0 PMID 30333628 S2CID 52987203 Krauss Lawrence M 2012 A Universe from Nothing Free Press p 82 ISBN 9781451624458 What Do You Mean The Universe Is Flat Part I Scientific American Davide Castelvecchi July 25 2011 Peebles P J E 1993 Principles of Physical Cosmology Princeton University Press p 73 ISBN 9780691019338 Rothstein Dave 23 April 2003 What is the universe expanding into Ask an Astronomer Retrieved 28 April 2017 Pons J M Talavera P 2021 On cosmological expansion and local physics General Relativity and Gravitation 53 11 105 arXiv 2011 01216 Bibcode 2021GReGr 53 105P doi 10 1007 s10714 021 02874 4 S2CID 226236696 Tamara M Davis and Charles H Lineweaver Expanding Confusion common misconceptions of cosmological horizons and the superluminal expansion of the universe astro ph 0310808 Alan B Whiting 2004 The Expansion of Space Free Particle Motion and the Cosmological Redshift The Observatory 124 174 arXiv astro ph 0404095 Bibcode 2004Obs 124 174W EF Bunn amp DW Hogg 2009 The kinematic origin of the cosmological redshift American Journal of Physics 77 8 688 694 arXiv 0808 1081 Bibcode 2009AmJPh 77 688B doi 10 1119 1 3129103 S2CID 1365918 Yu V Baryshev 2008 Expanding Space The Root of Conceptual Problems of the Cosmological Physics Practical Cosmology 2 20 30 arXiv 0810 0153 Bibcode 2008pc2 conf 20B JA Peacock 2008 A diatribe on expanding space arXiv 0809 4573 astro ph Friedman A Uber die Krummung des Raumes Z Phys 10 1922 377 386 English translation in Gen Rel Grav 31 1999 1991 2000 Hubble Edwin 1936 Effects of Red Shifts on the Distribution of Nebulae The Astrophysical Journal 84 11 621 627 Bibcode 1936ApJ 84 517H doi 10 1086 143782 PMC 1076828 PMID 16577738 Hubble Edwin 1937 Red shifts and the distribution of nebulae Monthly Notices of the Royal Astronomical Society 97 7 506 Bibcode 1937MNRAS 97 506H doi 10 1093 mnras 97 7 506 Gingerich Owen 1999 A Brief History of Our View of the Universe Publ Astron Soc Pac Astronomical Society of the Pacific 111 757 254 257 Bibcode 1999PASP 111 254G doi 10 1086 316324 JSTOR 10 1086 316324 a b c Overbye Dennis 20 February 2017 Cosmos Controversy The Universe Is Expanding but How Fast The New York Times ISSN 0362 4331 Retrieved 29 June 2017 Interview with Alan Guth THE INFLATIONARY UNIVERSE 11 19 02 by Edge org 1 Bennett Charles L 27 April 2006 Cosmology from start to finish Nature 440 7088 1126 1131 Bibcode 2006Natur 440 1126B doi 10 1038 nature04803 PMID 16641983 S2CID 4371349 Hubble Edwin A Relation between Distance and Radial Velocity among Extra Galactic Nebulae 1929 Proceedings of the National Academy of Sciences of the United States of America Volume 15 Issue 3 pp 168 173 Full article PDF Astronomers reported their measurement in a paper published in the December 2000 issue of Nature titled The microwave background temperature at the redshift of 2 33771 which can be read here 2 A press release from the European Southern Observatory explains the findings to the public Direct detection of the cosmic expansion the redshift drift and the flux driftPrinted references EditEddington Arthur The Expanding Universe Astronomy s Great Debate 1900 1931 Press Syndicate of the University of Cambridge 1933 Liddle Andrew R and David H Lyth Cosmological Inflation and Large Scale Structure Cambridge University Press 2000 Lineweaver Charles H and Tamara M Davis Misconceptions about the Big Bang Scientific American March 2005 non free content Mook Delo E and Thomas Vargish Inside Relativity Princeton University Press 1991 External links Edit Wikimedia Commons has media related to Expansion of the universe Swenson Jim Answer to a question about the expanding universe Archived 11 January 2009 at the Wayback Machine Felder Gary The Expanding universe NASA s WMAP team offers an Explanation of the universal expansion at a very elementary level Hubble Tutorial from the University of Wisconsin Physics Department Archived 9 June 2014 at the Wayback Machine Expanding raisin bread from the University of Winnipeg an illustration but no explanation Ant on a balloon analogy to explain the expanding universe at Ask an Astronomer The astronomer who provides this explanation is not specified Portals Physics Astronomy Stars Spaceflight Solar System Retrieved from https en wikipedia org w index php title Expansion of the universe amp oldid 1152494874, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.