fbpx
Wikipedia

Paul Steinhardt

January 01, 1970

Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist whose principal research is in cosmology and condensed matter physics. He is currently the Albert Einstein Professor in Science at Princeton University, where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences.[3]

Paul Steinhardt
Born
Paul Joseph Steinhardt

(1952-12-25) December 25, 1952 (age 71)
Washington, D.C., US
Alma mater
Known for
Awards
Scientific career
FieldsTheoretical physics
Cosmology
Condensed Matter Physics
Institutions
ThesisLattice theory of SU(N) flavor quantum electrodynamics in (1 + 1)-dimensions (1978)
Doctoral advisorSidney R. Coleman[1]
Other academic advisors
Doctoral students
Websitepaulsteinhardt.org

Steinhardt is best known for his development of new theories of the origin, evolution and future of the universe. He is also well known for his exploration of a new form of matter, known as quasicrystals, which were thought to exist only as man-made materials until he co-discovered the first known natural quasicrystal in a museum sample.[4] He subsequently led a separate team that followed up that discovery with several more examples of natural quasicrystals recovered from the wilds of the Kamchatka Peninsula in far eastern Russia. Several years later, he and collaborators reported the accidental synthesis of a previously unknown type of quasicrystal in the remnants of the first atomic bomb test on July 16, 1945, at Alamagordo, New Mexico.[5]

He has written two popular books on these topics. Endless Universe: Beyond the Big Bang (2007), co-authored with Neil Turok, describes the early struggles in challenging the widely accepted big bang theory and the subsequent development of the bouncing or cyclic theories of the universe, which are currently being explored and tested.[6] The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter (2019) recounts the story of quasicrystals from his invention of the concept with his then-student Dov Levine, to his expedition to far eastern Russia to recover meteorite fragments containing natural quasicrystal grains formed billions of years ago.[7]

Education and career edit

Born in 1952 to Helen and Charles Steinhardt, Paul Steinhardt is the second oldest of four children. He grew up in Miami, Florida, where he attended Coral Gables Senior High School while attending classes at a local university. Steinhardt received his Bachelor of Science in Physics at Caltech in 1974, and his Ph.D. in Physics at Harvard University in 1978 where his advisor was Sidney Coleman.[1] He was a Junior Fellow in the Harvard Society of Fellows from 1978 to 1981; rose from junior faculty to Mary Amanda Wood Professor at the University of Pennsylvania between 1981 and 1998, during which he maintained a long-term association with the Thomas J. Watson Research Center; and has been on the faculty at Princeton University since the Fall of 1998. He co-founded the Princeton Center for Theoretical Science and served as its Director from 2007 to 2019.[8]

Research edit

Inflationary cosmology edit

Beginning in the early 1980s, Steinhardt co-authored seminal papers that helped to lay the foundations of inflationary cosmology.

 
Steinhardt at University of Pennsylvania

Slow-roll inflation and Generation of the seeds for galaxies: In 1982, Steinhardt and Andreas Albrecht[9] (and, independently, Andrei Linde) constructed the first inflationary models that could speed up the expansion of the universe enough to explain the observed smoothness and flatness of the universe and then "gracefully exit" to the more modest expansion observed today.[10] The Albrecht-Steinhardt paper was the first to note the effect of Hubble friction in sustaining inflation for a sufficiently long period (the "slow-roll" effect), setting the prototype for most subsequent inflationary models.

Hubble friction played a critical role in the 1983 paper by James Bardeen, Steinhardt and Michael S. Turner[11] who were the first to introduce a reliable, relativistically gauge invariant method to compute how quantum fluctuations during inflation might naturally generate a nearly scale-invariant spectrum of density fluctuations with a small tilt, properties later shown by observations of the cosmic microwave background to be features of our universe. The density fluctuations are seeds about which galaxies eventually form. Contemporaneous calculations by several other groups obtained similar conclusions using less rigorous methods.

Eternal inflation and the multiverse: In 1982, Steinhardt presented the first example of eternal inflation.[12] Neverending inflation was eventually shown to be a generic feature of inflationary models that leads to a multiverse, the break-up of space into an infinite multitude of patches spanning an infinite range of outcomes instead of the single smooth and flat universe, as originally hoped when first proposed.

Although some cosmologists would later come to embrace the multiverse, Steinhardt consistently expressed his concern that it utterly destroys the predictive power of the theory he helped create. Because the inflationary theory leads to a multiverse that allows for every possible outcome, Steinhardt argued, we must conclude that the inflationary theory actually predicts nothing.[13][14][15]

Imprint of gravitational waves on the cosmic microwave background: In 1993, Robert Crittenden, Rick Davis, J.R. Bond, G. Efstathiou and Steinhardt performed the first calculations of the complete imprint of gravitational waves on the B-mode temperature maps and on the polarization of the microwave background radiation in 1993.[16][17]

Despite his criticisms of the idea, Steinhardt's major contributions to the inflationary theory were recognized in 2002 when he shared the Dirac Prize with Alan Guth of M.I.T. and Andrei Linde of Stanford.[18]

The unlikeliness problem: In 2013, Anna Ijjas, Abraham Loeb and Steinhardt added to the criticisms in a widely discussed pair of papers that the inflationary model was much less likely to explain our universe than previously thought.[19][20]

According to their analysis of the Planck satellite 2013 results, the chances of obtaining a universe matching the observations after a period of inflation is less than one in a googolplex.[21] Steinhardt and his team dubbed the result the "unlikeliness problem." The two papers also showed that Planck satellite data ruled out what had been historically accepted as the simplest inflationary models and that the remaining inflationary models require more parameters, more fine-tuning of those parameters, and more unlikely initial conditions.[19][20]

In 2015, the unlikeness problem was reaffirmed and strengthened by a subsequent round of measurements reported by the Planck satellite team.

Incompatibility with the string-swampland conjectures: In 2018, Steinhardt, in collaboration with Prateek Agrawal, George Obieds, and Cumrun Vafa, argued that inflation may also be incompatible with string theory because inflationary models generally violate constraints (sometimes called the "swampland conjectures") on what is required for a model to be consistent with quantum gravity.[22]

Bouncing and cyclic cosmology edit

Motivated by what he viewed as the failures of inflationary theory, including but not limited to the multiverse, Steinhardt became a leading developer of a new class of cosmological models that replace the so-called big bang with a bounce and replace inflation with a period of slow contraction preceding the bounce. The hypothetical idea that the universe began with a bang is based on extrapolating back in time, assuming that Einstein's equations of general relativity remain valid at energies and temperatures far greater than have ever been tested.

Theorists generally agree that, if there was a big bang, then, in the instants following, quantum physics effects should have created large fluctuations in spacetime. These fluctuations would have caused space-time to curve and warp and the distribution of energy to become very uneven, all of which is inconsistent with what experimentalists observe when they study the early universe. The universe is, in fact, observed to be homogeneous. [23] Inflation was originally invented to expain the smoothness that is observed in the universe. But it is unclear how to transition from the highy uneven conditions created after a big bang to an inflationary universe and, even if a solution could be found, the inflationary theory ultimately results in a multiverse rather than a smooth universe.[15]

The new approach removes the bang altogether, envisioning instead a smooth transition from a previous period of slow contraction to the current period of expansion. If the contraction is slow, it smooths the entire universe, and, unlike inflation there is no multiverse. By evading the infamous cosmic singularity problem associated with a big bang, a bounce avoids quantum gravity effects that produce an unsmooth universe. A natural extension of these ideas is a never-beginning and never-ending cyclic universe in which epochs of bounce, expansion, and contraction repeat at regular intervals.

In a pivotal lecture in 2021, Steinhardt explained why it is time to jettison the big bang theory and replace the bang with a ‘bounce’ — a smooth transition from contraction to a dense, hot universe that continues to expand and cool. [24]

Historical Development

Early models with a big crunch: In 2001, Steinhardt presented the first examples of these bouncing and cyclic models, referred to as "ekpyrotic," in papers with Justin Khoury, Burt A. Ovrut and Neil Turok.[25]

These models were based on the speculative notion suggested by string theory that the universe has extra-dimensions bounded by "branes" (where "brane" is derived from "membrane," a basic object in string theory). The fiery collision and rebound of these branes is comarable to a big crunch, a violent event that would depend sensitively on strong quantum gravity effects that are not yet established and may create tremendous curvature and warping of spacetime.

In principle, the collisions can repeat at regular intervals resulting in a cyclic universe.[15] In 2002, Steinhardt and Turok incorporated the ekpyrotic idea into an early version of a cyclic theory of the universe.[26]

Improved models with slow contraction and a gentle bounce: Recent versions of bouncing cosmology developed by Anna Ijjas and Steinhardt introduce elements that simplify and address problems with the earlier ekpyrotic proposal. They do not require extra dimensions or branes or string theory; ordinary fields with potential energy evolving in space-time, similar to inflationary models, can be used. [27]

Instead of a violent ekpyrosis (the collision of two branes), the smoothing and flattening of spacetime occurs through ``slow contraction,” a period in which space contracts very little while the Hubble radius contracts a lot. By the time the bounce is reached, the universe is ``supersmoothed.” [28]

The bounce is a gentle transition that can be fully computed and maintains smoothness because it is a continuoous process that occurs long before quantum gravity effects become strong. There is no cosmic singularity problem, unlike theories based on the big bang.

Universal smoothing and ultralocality: To test these ideas, Anna Ijjas adapted the tools of numerical general relativity, originally invented to simulate the merger of black holes and the emission of gravitational waves, to cosmology. Together with Steinhardt and collaborators, the new tools were used to study the effectiveness of slow contraction. [28] [29] [30]

The study demonstrates that slow contraction is a supersmoothing cosmological phase that homogenizes, isotropizes and flattens the universe both classically and quantum mechanically and can do so far more robustly and rapidly than had been realized in earlier studies.

Beginning from wildly unsmooth and curvy starting condition, the studies verified that slow contraction smooths virtually all of spacetime due to an effect of general relativity known as ultralocality. [31] The ultralocal effect is specific to a contracting universe, and there is no equivalent in an expanding universe, including the case of inflation. The consequent smoothing power is an unparalleled advantage of slow contraction.

Cyclic version of bouncing cosmology: In the cyclic version of these models, space never crunches; rather, it necessarily grows by a constant factor overall from bounce to bounce every 100 billion years or so. After each bounce, gravitational energy is converted into the matter and radiation that fuels the next cycle. To an observer, the evolution appears to be cyclic because the temperature, density, number of stars and galaxies, etc., are on average the same from one cyclic to the next and the observer cannot see far enough to know that there is the observer cannot see far enough to know that there is an ever-increasing amount of space, matter energy outside the horizon. The fact that the universe expands overall from cycle to cycle means that the entropy produced in earlier cycles (by the formation of stars and other entropy-producing processes) is increasingly diluted as the cycles proceed and so does not have any physical effect on cosmic evolution.[27] This growth from cycle to cycle and associated entropy dilution are features that distinguish these new cyclic models from versions discussed in the 1920s by Friedmann and Tolman, and explain how the new cyclic model avoids the "entropy problem" that beset earlier versions.

Theoretical advantages of the new cyclic model

The new cyclic models have two important advantages over inflationary models. First, because they do not include inflation, they do not produce a multiverse. As a result, unlike inflation, cyclic models produce a single universe that everywhere have the same predicted properties that are subject to empirical tests. Second, cyclic models explain why there must be dark energy. According to these models, the accelerated expansion caused by dark energy starts the smoothing process, the decay of dark energy to other forms of energy starts a period of slow contraction, and the slow contraction is what is responsible for smoothing and flattening the universe.[27]

Theoretical predictions of the new cyclic model

One prediction of the cyclic models is that, unlike inflation, no detectable gravitational waves are generated during the smoothing and flattening process. The Simons Observatory being built in the Atacama Desert in Chile will test this prediction. Instead, the prediction of the cyclic models is that the only source of gravitational waves on cosmic wavelength scales are so-called "secondary gravitational waves" that are produced long after the bounce. Their amplitudes are far too weak to be found in current detectors but are ultimately detectable. A second prediction is that the current acceleration expansion must eventually stop and the vacuum must be eventually decay in order to initiate the next cycle.[27](Other predictions depend on the specific fields (or branes) that cause the contraction.)

Observational support for the new cyclic model

The cyclic model may naturally explain why the cosmological constant is exponentially small and positive, compared to the enormous value expected by quantum gravity theories.[32] The cosmological constant might begin large, as expected, but then might slowly decay over the course of many cycles to the tiny value observed today.

The discovery of the Higgs field at the Large Hadron Collider (LHC) may provide added support for the cyclic model.[33] Evidence from the LHC suggests that the current vacuum may decay in the future, according to calculations made by Steinhardt, Turok and Itzhak Bars. The decay of the current vacuum is required by the cyclic model in order to end the current phase of expansion, contract, bounce and begin a new era of expansion; the Higgs provides a possible mechanism of decay that can be tested. The Higgs field is a viable candidate for the field that drives the cycles of expansion and contraction, and this may ultimately be testable.

Dark energy and dark matter edit

Steinhardt has made significant contributions researching the "dark side" of the universe: dark energy, the cosmological constant problem and dark matter.

First evidence of cosmic acceleration: In 1995, Steinhardt and Jeremiah Ostriker used a concordance of cosmological observations to show there must be a non-zero dark energy component today, more than 65 percent of the total energy density, sufficient to cause the expansion of the universe to accelerate.[34] This was verified three years later by supernova observations in 1998.[35][36][37]

Quintessence: Working with colleagues, he subsequently introduced the concept of quintessence, a form of dark energy that varies with time.[38] It was first posited by Steinhardt's team as an alternative to the cosmological constant, which is (by definition) constant and static; quintessence is dynamic. Its energy density and pressure evolve over time. The 2018 paper on swampland conjectures with Agrawal, Obieds and Vafa[22] points to quintessence as being the only option for dark energy in string theory and consistent quantum gravity.

Self-interacting dark matter: In 2000, David Spergel and Steinhardt first introduced the concept of strongly self-interacting dark matter (SIDM) to explain various anomalies in standard cold dark models based on assuming dark matter consists of weakly interacting massive particles (also referred to as "WIMPs").[39]

In 2014, Steinhardt, Spergel and Jason Pollack have proposed that a small fraction of dark matter could have ultra-strong self-interactions, which would cause the particles to coalesce rapidly and collapse into seeds for early supermassive black holes.[40]

Quasicrystals edit

Development of the theory: In 1983, Steinhardt and his then-student Dov Levine first introduced the theoretical concept of quasicrystals in a patent disclosure.[7] The complete theory was published the following year in a paper entitled "Quasicrystals: A New Class of Ordered Structures."[41] The theory proposed the existence of a new phase of solid matter analogous to Penrose tilings with rotational symmetries previously thought to be impossible for solids. Steinhardt and Levine named the new phase of matter a "quasicrystal." The never-before-seen atomic structure had quasiperiodic atomic ordering, rather than the periodic ordering characteristic of conventional crystals.

The new theory overturned 200 years of scientific dogma and proved that quasicrystals could violate all of the previously accepted mathematical theorems about the symmetry of matter. Symmetries once thought to be forbidden for solids are actually possible for quasicrystals, including solids with axes of five-fold symmetry and three-dimensional icosahedral symmetry.

The first reported example of a synthetic quasicrystal: Working simultaneously to, but independently of, Steinhardt and Levine, Dan Shechtman, Ilan Blech, Denis Gratias and John Cahn at the National Bureau of Standards (NBS) were focused on an experimental discovery they could not explain. It was an unusual alloy of manganese and aluminum with a diffraction pattern of what appeared to be sharp (though not perfectly point-like) spots arranged with icosahedral symmetry that did not fit any known crystal structure.[42] The alloy was first noted in 1982, but results were not published until November 1984 after more convincing data had been obtained.[7]

Steinhardt and Levine were shown a preprint of the Shechtman team's paper and immediately recognized that it could be experimental proof of their still-unpublished quasicrystal theory.[7] The theory, along with the proposal that it could explain the mysterious, forbidden structure of the new alloy was published in December 1984.[41]

The new alloy was ultimately discovered to be problematic. It proved to be unstable and the noted imperfections in the diffraction pattern allowed for multiple explanations (including one about crystal twinning proposed by Linus Pauling) that were hotly debated for the next few years.[7] In 1987, An-Pang Tsai and his group at Japan's Tohoku University made an important breakthrough with the synthesis of the first-ever stable icosahedral quasicrystal. It had sharp diffraction spots arranged in close accord with Steinhardt and Levine's quasicrystal theory and was inconsistent with any of the alternative explanations.[43] The theoretical debate was effectively ended and the Steinhardt-Levine theory gained wide acceptance.[7]

 
Small sample, about 3 mm across, of a Khatyrkite-bearing meteorite (top and bottom left panels)from the mineral collection at the Museo di Storia Naturale in Florence, Italy. On January 2, 2009, Paul Steinhardt and Nan Yao identified the first known natural quasicrystal embedded in the sample (area of discovery indicated by red circle in bottom right panel).

The first natural quasicrystal: In 1999, Steinhardt assembled a team at Princeton University to search for a natural quasicrystal. The team, composed of Peter Lu, Ken Deffeyes and Nan Yao, devised a novel mathematical algorithm to search through an international database of powder diffraction patterns.[7][44]

For the first eight years, the search yielded no results. In 2007, Italian scientist Luca Bindi, then curator of the mineral collection at the Universite’ di Firenze, joined the team.[7] Two years later, Bindi identified a promising specimen in his museum's storage room.[4] The tiny specimen, a few millimeters across, had been packed away in a box labeled "khatyrkite," which is an ordinary crystal composed of copper and aluminum. On January 2, 2009, Steinhardt and Nan Yao, director of the Princeton Imaging Center, examined the material and identified the signature diffraction pattern of an icosahedral quasicrystal. This was the first known natural quasicrystal.[4]

 
The electron diffraction pattern for icosahedrite, the first natural quasicrystal, obtained by aiming the electron beam down a fivefold axis of symmetry. The patterns correspond perfectly (up to experimental resolution) with the fivefold patterns first predicted by Paul Steinhardt and Dov Levine in the 1980s for an icosahedral quasicrystal.

The International Mineralogical Association accepted the quasicrystal as a new mineral and designated its name, icosahedrite.[4] The material had exactly the same atomic composition (Al63Cu24Fe13) as the first thermodynamically stable quasicrystal synthesized by An-Pang Tsai and his group in their laboratory in 1987.

Expedition to Chukotka: Two years after identifying the museum sample, Steinhardt organized an international team of experts and led them on an expedition to its source, the remote Listventovyi stream in the Chukotka Autonomous Okrug in the northern half of the Kamchatka Peninsula in far eastern Russia. The team included Bindi and Valery Kryachko, the Russian ore geologist who had found the original samples of khatyrkite crystal while working at the Listventovyi stream in 1979.[7]

 
On location at the Listventovyi stream in the Kamchatka Peninsula in 2011 (left to right): Luca Bindi (University of Firenze, Italy), Valery Kryachko (IGEM, Russia) and Paul Steinhardt (Princeton, USA)

Other members of the team were: Chris Andronicos, Vadim Distler, Michael Eddy, Alexander Kostin, Glenn MacPherson, Marina Yudovskaya, and Steinhardt's son, William Steinhardt.[7]

After digging and panning a ton and a half of clay along the banks of the Listvenitovyi stream in the Koryak Mountains, eight different grains containing icosahedrite were identified.[7] During subsequent years of study, Steinhardt's team proved that both the sample found in the Florence museum and the samples recovered from the field in Chukotka originated from a meteorite formed 4.5 billion years ago (before there were planets), and landed on the Earth about 15,000 years ago.[45]

More natural quasicrystals: Further studies revealed other new minerals in the Chukotka samples. In 2014, one of those minerals was discovered to be a crystalline phase of aluminum, nickel and iron (Al38Ni33Fe30). It was accepted by the International Mineralogical Association and named "steinhardtite" in Steinhardt's honor[46] In 2015, a second type of natural quasicrystal was discovered in a different grain of the same meteorite. The second known natural quasicrystal was found to be a different mixture of aluminum, nickel and iron (Al71Ni24Fe5) and had a decagonal symmetry (a regularly stacking of atomic layers which each have 10-fold symmetry). It was accepted by the International Mineralogical Association and given the name "decagonite."[47][48]

Three more crystalline minerals were also discovered and named after colleagues involved in Steinhardt's quasicrystal research: "hollisterite," for Princeton petrologist Lincoln Hollister; "kryachkoite," for Russian geologist Valery Kryachko; and "stolperite," for Caltech's former provost Ed Stolper.[7]

 
Girih tile quasicrystal pattern on right half of spandrel at Darb-e Imam Shrine

A previously unknown quasicrystal created by the first atomic bomb test: In 2021, Steinhardt led the team that discovered a novel icosahedral quasicrystal created by the detonation of the first nuclear device at Alamogordo, New Mexico, on July 16, 1945 (the Trinity test). The new quasicrystal was discovered within a sample of red trinitite and is the oldest extant anthropogenic quasicrystal ever discovered.[5] The previously unknown structure, which is made of iron, silicon, copper and calcium, is thought to have been formed by the fusion of vaporized desert sand and copper cables during the atomic test blast.[49] The discovery of a unique quasicrystal in trinitite could transform the field of nuclear forensics, leading to a new diagnostic tool[50] which could help law enforcement prevent future terrorist attacks by using quasicrystals (which unlike radioactive debris and gases do not decay) to identify the signature of an atomic weapon and track down the culprits.[51]

Other contributions to the field: Steinhardt and his collaborators have made significant contributions to understanding the quasicrystals’ unique mathematical and physical properties,[52] including theories of how and why quasicrystals form[53] and their elastic and hydrodynamics properties.[54]

Peter J. Lu and Steinhardt discovered a quasicrystalline Islamic tiling on the Darb-e Imam Shrine (1453 A.D.) in Isfahan, Iran constructed from girih tiles.[55] In 2007, they deciphered the manner in which early artists created increasingly complex periodic girih patterns. Those early designs were shown to have culminated in the development of a nearly perfect quasi-crystalline pattern five centuries before the discovery of Penrose patterns and the Steinhardt-Levine quasicrystal theory.[7]

Photonics and hyperuniformity edit

Steinhardt's research on quasicrystals and other non-crystalline solids expanded into work on designer materials with novel photonic and phononic properties.

Photonic quasicrystals: A team of researchers including Steinhardt, Paul Chaikin, Weining Man and Mischa Megens designed and tested the first photonic quasicrystal with icosahedral symmetry in 2005. They were the first to demonstrate the existence of photonic band gaps ("PBGs").[56] These materials block light for a finite range of frequencies (or colors) and let pass light with frequencies outside that band, similar to the way in which a semiconductor blocks electrons for a finite range of energies.

Hyperuniform disordered solids (HUDS): Working with Salvatore Torquato and Marian Florescu, in 2009 Steinhardt discovered a new class of photonic materials called hyperuniform disordered solids (HUDS), and showed that solids consisting of a hyperuniform disordered arrangement of dielectric elements produce band gaps with perfect spherical symmetry.[57][58] These materials, which act as isotropic semiconductors for light, can be used to control and manipulate light in a wide range of applications including optical communications, photonic computers, energy harvesting, non-linear optics and improved light sources.

Phoamtonics: In 2019, Steinhardt, along with Michael Klatt and Torquato, introduced the idea of "phoamtonics," which refers to photonic materials based on foam-like designs.[59] They showed that large photonic bandgaps could arise in network structures created by converting the foam edges (intersections between foam bubbles) to a dielectric material for the two most famous crystalline foam structures, Kelvin foams and Weiare-Phelan foams.

Etaphase Inc.: The meta-material breakthroughs by Steinhardt and his Princeton colleagues have valuable commercial applications. In 2012, the scientists helped create a start-up company called Etaphase, which will apply their discoveries to a wide range of high performance products. The inventions will be used in integrated circuits, structural materials, photonics, communications, chip-to-chip communications, intra-chip communications, sensors, datacomm, networking, and solar applications.[60][61]

Amorphous solids edit

Steinhardt's research in disordered forms of matter has centered on the structure and properties of glasses and amorphous semiconductors, and amorphous metals.

He constructed the first computer generated continuous random network (CRN) model of glass and amorphous silicon in 1973, while still an undergraduate at Caltech. CRNs remain the leading model of amorphous silicon and other semiconductors today. Working with Richard Alben and D. Weaire, he used the computer model to predict structural and electronic properties.[62][63]

Working with David Nelson and Marco Ronchetti, Steinhardt formulated mathematical expressions, known as "orientational order parameters", for computing the degree of alignment of interatomic bonds in liquids and solids in 1981. Applying them to computer simulations of monatomic supercooled liquids, they showed that the atoms form arrangements with finite-range icosahedral (soccer-ball like) bond orientational order as liquids cool.

Honors and awards edit

References edit

  1. ^ a b c Paul Steinhardt at the Mathematics Genealogy Project  
  2. ^ Mack, Katherine J. (2009). Tests of early universe physics from observational astronomy (Thesis). ProQuest 304982499.
  3. ^ "Biographical Sketch: Prof. Paul J. Steinhardt". Department of Physics at Princeton University. Retrieved January 29, 2019.
  4. ^ a b c d Bindi, L.; Steinhardt, P.J.; Yao, N.; Lu, P. (2009). "Natural Quasicrystals". Science. 324 (5932): 1306–1309. Bibcode:2009Sci...324.1306B. doi:10.1126/science.1170827. PMID 19498165. S2CID 14512017.
  5. ^ a b Bindi, Luca; Kolb, William; Eby, G. Nelson; Asimow, Paul D.; Wallace, Terry C.; Steinhardt, Paul J. (2021). "Accidental synthesis of a previously unknown quasicrystal in the first atomic bomb test". PNAS. 118 (June 1, 2021 118 (22) e2101350118): e2101350118. Bibcode:2021PNAS..11801350B. doi:10.1073/pnas.2101350118. PMC 8179242. PMID 34001665.
  6. ^ Steinhardt, P.J.; Turok, N.G. (2007). Endless Universe: beyond the Big Bang. Doubleday. ISBN 9780385509640.
  7. ^ a b c d e f g h i j k l m Steinhardt, P.J. (2019). The Second Kind of Impossible. Simon & Schuster. ISBN 9781476729923.
  8. ^ "Paul Steinhardt Bio". Paul Steinhardt. Retrieved 26 June 2019.
  9. ^ Albrecht, A.; Steinhardt, P. J. (1982). "Cosmology For Grand Unified Theories With Radiatively Induced Symmetry Breaking". Phys. Rev. Lett. 48 (17): 1220–1223. Bibcode:1982PhRvL..48.1220A. doi:10.1103/PhysRevLett.48.1220.
  10. ^ Albrecht, A.; Steinhardt, P.J. (1982). "Reheating an Inflationary Universe". Phys. Rev. Lett. 48 (20): 1437–1440. Bibcode:1982PhRvL..48.1437A. doi:10.1103/PhysRevLett.48.1437.
  11. ^ Bardeen, J. M.; Steinhardt, P. J.; Turner, M. S. (1983). "Spontaneous Creation Of Almost Scale-Free Density Perturbations In An Inflationary Universe". Phys. Rev. D. 28 (4): 679–693. Bibcode:1983PhRvD..28..679B. doi:10.1103/PhysRevD.28.679.
  12. ^ Gibbons, Gary W.; Hawking, Stephen W.; Siklos, S.T.C., eds. (1983). "Natural Inflation". The Very Early Universe. Cambridge University Press. pp. 251–66. ISBN 978-0-521-31677-4.
  13. ^ Steinhardt, Paul J. (April 2011). "Inflation Debate: Is the theory at the heart of modern cosmology deeply flawed?" (PDF). Scientific American. 304 (4): 36–43. Bibcode:2011SciAm.304d..36S. doi:10.1038/scientificamerican0411-36. PMID 21495480.
  14. ^ Steinhardt, Paul J. "The Cyclic Theory of the Universe" (PDF). www.prsinstitute.org. Retrieved 4 November 2023.
  15. ^ a b c Horgan; John (December 1, 2014), "Physicist Slams Cosmic Theory He Helped Conceive", Scientific American
  16. ^ Crittenden, R.; Bond, J.R.; Davis, R.L.; Efstathiou, G.E.; Steinhardt, P. J. (1993). "The Imprint of Gravitational Waves on the Cosmic Microwave Background". Phys. Rev. Lett. 71 (3): 324–327. arXiv:astro-ph/9303014. Bibcode:1993PhRvL..71..324C. doi:10.1103/PhysRevLett.71.324. PMID 10055242. S2CID 18553924.
  17. ^ Crittenden; Davis, R.L.; Steinhardt, P. J. (1993). "Polarization of the Microwave Background due to Primordial Gravitational Waves". Astrophysical Journal Letters. 417: L13–L16. arXiv:astro-ph/9306027. Bibcode:1993ApJ...417L..13C. doi:10.1086/187082. S2CID 18194291.
  18. ^ a b "ICTP - International Centre for Theoretical Physics". www.ictp.it. Retrieved 28 January 2019.
  19. ^ a b Iijas, Anna; Loeb, Abraham; Steinhardt, Paul (2013). "Inflationary Paradigm in trouble after Planck 2013". Phys. Lett. B. 723 (4–5): 261–266. arXiv:1304.2785. Bibcode:2013PhLB..723..261I. doi:10.1016/j.physletb.2013.05.023. S2CID 14875751.
  20. ^ a b Iijas, Anna; Steinhardt, Paul J.; Loeb, Abraham (2014). "Inflationary Schism". Phys. Lett. B. 7: 142–146. arXiv:1402.6980. Bibcode:2014PhLB..736..142I. doi:10.1016/j.physletb.2014.07.012. S2CID 119096427.
  21. ^ "Filling the Big Gap in Einstein's Theory, Paul Steinhardt TEDxCLESalon". YouTube. Retrieved September 21, 2016.
  22. ^ a b Obied, Georges; Ooguri, Hirosi; Steinhardt, Paul J. (2018). "On the Cosmological Implications of the String Swampland". Phys. Lett. B. 784: 271–276. arXiv:1806.09718. Bibcode:2018PhLB..784..271A. doi:10.1016/j.physletb.2018.07.040. S2CID 119252887.
  23. ^ "Planck reveals an almost perfect Universe". ESA. Retrieved January 21, 2024.
  24. ^ "Paul Steinhardt – Time to Take the 'Big Bang' out of the Big Bang Theory?". YouTube. Retrieved January 21, 2024.
  25. ^ Khoury, J.; Ovrut, B.; Steinhardt, P. J. (2001). "The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang". Phys. Rev. D. 64 (12): 123522. arXiv:hep-th/0103239. Bibcode:2001PhRvD..64l3522K. doi:10.1103/PhysRevD.64.123522. S2CID 374628.
  26. ^ Steinhardt, P. J.; Turok, N. (2002-04-25). "A Cyclic Model of the Universe". Science. 296 (5572): 1436–1439. arXiv:hep-th/0111030. Bibcode:2002Sci...296.1436S. doi:10.1126/science.1070462. PMID 11976408. S2CID 1346107.
  27. ^ a b c d Ijjas, Anna; Steinhardt, Paul J. (2019). "A new kind of cyclic universe". Phys. Lett. B. 795: 666–672. arXiv:1904.08022. Bibcode:2019PhLB..795..666I. doi:10.1016/j.physletb.2019.06.056. S2CID 118712442.
  28. ^ a b Cook, William G.; Glushchenko, Iryna A.; Ijjas, Anna; Pretorius, Franz; Steinhardt, Paul J. (2020). "Supersmoothing through Slow Contraction". Phys. Lett. B. 808. arXiv:2006.01172. doi:10.1016/j.physletb.2020.135690.
  29. ^ Ijjas, Anna; Cook, William G.; Pretorius, Franz; Steinhardt, Paul J.; Davies, Elliot Y. (2020). "Robustness of slow contraction to cosmic initial conditions". JCAP. 2020. arXiv:2006.04999v2. doi:10.1088/1475-7516/2020/08/030.
  30. ^ Garfinkle, David; Ijjas, Anna; Steinhardt, Paul J. (2023). "Initial conditions problem in cosmological inflation revisited". Phys. Lett. B. 843. arXiv:2304.12150. doi:10.1016/j.physletb.2023.13802.
  31. ^ Ijjas, Anna; Sullivan, Andrew P.; Pretorius, Frans; Steinhardt, Paul J.; Cook, William G. (2021). "Ultralocality and Slow Contraction". JCAP. 2021. arXiv:2103.00584v1. doi:10.1088/1475-7516/2021/06/013.
  32. ^ Steinhardt, P. J.; Turok, N. (2006). "Why the cosmological constant is small and positive". Science. 312 (5777): 1180–1182. arXiv:astro-ph/0605173. Bibcode:2006Sci...312.1180S. doi:10.1126/science.1126231. PMID 16675662. S2CID 14178620.
  33. ^ Bars, I.; Steinhardt, P.J.; Turok, N (2013). "Cyclic cosmology, conformal symmetry and the metastability of the Higgs". Phys. Lett. B. 726 (1–3): 50–55. arXiv:1307.8106. Bibcode:2013PhLB..726...50B. doi:10.1016/j.physletb.2013.08.071. S2CID 592287.
  34. ^ Ostriker, J. P.; Steinhardt, P.J. (1995). "The observational case for a low-density Universe with a non-zero cosmological constant". Nature. 377 (6550): 600–602. Bibcode:1995Natur.377..600O. doi:10.1038/377600a0. S2CID 4236645.
  35. ^ Riess, A.; al., et (1998). "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant". The Astronomical Journal. 116 (3): 1009–1038. arXiv:astro-ph/9805201. Bibcode:1998AJ....116.1009R. doi:10.1086/300499. S2CID 15640044.
  36. ^ Perlmutter, S.; al., et (1999). "Measurements of Omega and Lamba from 42 High-Redshift Supernovae". The Astrophysical Journal. 517 (2): 565–586. arXiv:astro-ph/9812133. Bibcode:1999ApJ...517..565P. doi:10.1086/307221. S2CID 118910636.
  37. ^ Bahcall, N.A.; Ostriker, J.P.; Perlmutter, S.; Steinhardt, P.J. (1999). "The Cosmic Triangle: Revealing the State of the Universe". Science. 284 (5419): 1481–1488. arXiv:astro-ph/9906463. Bibcode:1999Sci...284.1481B. doi:10.1126/science.284.5419.1481. S2CID 15271568.
  38. ^ Caldwell, R.R.; Dave, R.; Steinhardt, P.J. (1998). "Cosmological Imprint of an Energy Component with General Equation-of-State". Phys. Rev. Lett. 80 (8): 1582–1585. arXiv:astro-ph/9708069. Bibcode:1998PhRvL..80.1582C. doi:10.1103/PhysRevLett.80.1582. S2CID 597168.
  39. ^ Spergel, D.N.; Steinhardt, P.J. (2000). "Observational Evidence for Self-Interacting Cold Dark Matter". Phys. Rev. Lett. 84 (17): 3760–3763. arXiv:astro-ph/9909386. Bibcode:2000PhRvL..84.3760S. doi:10.1103/PhysRevLett.84.3760. PMID 11019199. S2CID 6669358.
  40. ^ Pollack, Jason; Spergel, David N.; Steinhardt, Paul J. (2014). "Supermassive Black Holes from Ultra-Strongly Self-Interacting Dark Matter". The Astrophysical Journal. 804 (2): 131. arXiv:1501.00017. Bibcode:2015ApJ...804..131P. doi:10.1088/0004-637X/804/2/131. S2CID 15916893.
  41. ^ a b Levine, D.; Steinhardt, P.J. (1984). "Quasicrystals: A New Class of Ordered Structures" (PDF). Phys. Rev. Lett. 53 (26): 2477–2480. Bibcode:1984PhRvL..53.2477L. doi:10.1103/PhysRevLett.53.2477.
  42. ^ Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W. (1984). "Metallic Phase with Long-Range Orientational Order and No Translational Symmetry". Phys. Rev. Lett. 53 (20): 1951–1953. Bibcode:1984PhRvL..53.1951S. doi:10.1103/PhysRevLett.53.1951.
  43. ^ Tsai, An-Pang; Inoue, Akihisa; Masumoto, Tsuyoshi (1987). "A Stable Quasicrystal in Al-Cu-Fe System". Japanese Journal of Applied Physics. 26 (Part 2, Number 9): L1505–L1507. Bibcode:1987JaJAP..26L1505T. doi:10.1143/JJAP.26.L1505. S2CID 98442801.
  44. ^ Lu, P.; Deffreyes, K.; Steinhardt, P.J.; Yao (2001). "Identifying and Indexing Icosahedral Quasicrystals from Powder Diffraction Patterns". Phys. Rev. Lett. 87 (27): 275507. arXiv:cond-mat/0108259. Bibcode:2001PhRvL..87A5507L. doi:10.1103/PhysRevLett.87.275507. PMID 11800896. S2CID 2814118.
  45. ^ Wolchover, Natalie (13 June 2014). "In a grain, a Glimpse of the Cosmos". Quanta Magazine. Retrieved October 11, 2015.
  46. ^ a b Williams, Professor Peter (July 1, 2014). "Letter to Luca Bindi" (PDF). School of Science and Health, Western Sydney University / Paul J. Steinhardt. Retrieved January 29, 2019.
  47. ^ Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J. (2015). "Natural quasicrystal with decagonal symmetry". Scientific Reports. 5: 9111. Bibcode:2015NatSR...5E9111B. doi:10.1038/srep09111. PMC 4357871. PMID 25765857.
  48. ^ "Decagonite, Al71Ni24Fe5, a quasicrystal with decagonal symmetry". American Mineralogist. 100 (10). October 2015. doi:10.2138/am-2015-5423. S2CID 101528286.
  49. ^ Castelvecchi, Davide (2021). "First nuclear detonation created 'impossible' quasicrystals". Nature. 593 (7860): 487. Bibcode:2021Natur.593..487C. doi:10.1038/d41586-021-01332-0. PMID 34007024. S2CID 234779438.
  50. ^ D’Agostino, Susan (9 June 2021). "What are atomic bomb quasicrystals, and why do they matter?". Bulletin of the Atomic Scientists. Retrieved June 13, 2021.
  51. ^ Sloan, Marisa. "The First Atomic Bomb Created This 'Forbidden' Quasicrystal". Discover Magazine. Retrieved July 25, 2021.
  52. ^ Socolar, J.; Steinhardt, P.J. (1986). "Quasicrystals II: Unit Cell Configurations" (PDF). Phys. Rev. B. 34 (2): 617–647. Bibcode:1986PhRvB..34..617S. doi:10.1103/PhysRevB.34.617. PMID 9939668.
  53. ^ Jeong, H.C.; Steinhardt, P.J. (1996). "A simpler approach to Penrose tiling with implications for quasicrystal formation". Nature. 382 (6590): 431–433. Bibcode:1996Natur.382..431S. doi:10.1038/382431a0. S2CID 4354819.
  54. ^ Levine, D.; Lubensky, T.; Ostlund, S.; Ramaswamy, S.; Steinhardt, P.J.; Toner, J. (1985). "Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals". Phys. Rev. Lett. 54 (14): 1520–1523. Bibcode:1985PhRvL..54.1520L. doi:10.1103/PhysRevLett.54.1520. PMID 10031060.
  55. ^ Lu, P.; Steinhardt, P.J. (2007). "Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture". Science. 315 (5815): 1106–1110. Bibcode:2007Sci...315.1106L. doi:10.1126/science.1135491. PMID 17322056. S2CID 10374218.
  56. ^ Man, W.; Megens, M.; Steinhardt, P.J.; Chaikin, P. (2005). "Experimental Measurement of the Photonic Properties of Icosahedral Quasicrystals". Nature. 436 (7053): 993–996. Bibcode:2005Natur.436..993M. doi:10.1038/nature03977. PMID 16107842. S2CID 4408304.
  57. ^ Florescu, M.; Torquato, S.; Steinhardt, Paul J. (2009). "Designer disordered materials with large, complete photonic band gaps". Proceedings of the National Academy of Sciences. 106 (49): 20658–20663. arXiv:1007.3554. Bibcode:2009PNAS..10620658F. doi:10.1073/pnas.0907744106. PMC 2777962. PMID 19918087.
  58. ^ Man, W.; al., et (2013). "Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids". Proceedings of the National Academy of Sciences. 110 (40): 15886–15891. arXiv:1311.2632. Bibcode:2013PNAS..11015886M. doi:10.1073/pnas.1307879110. PMC 3791749. PMID 24043795.
  59. ^ Klatt, Michael A.; Torquato, Salvatore; Steinhardt, Paul J. (2019). "Phoamtonic designs yield sizeable 3D photonic band gaps". Proceedings of the National Academy of Sciences. 116 (47): 23480–23486. Bibcode:2019PNAS..11623480K. doi:10.1073/pnas.1912730116. PMC 6876150. PMID 31694882.
  60. ^ "Etaphase Incorporated". Etaphase Incorporated. Retrieved 28 January 2019.
  61. ^ "Advancing photonic functionalities" (PDF). torquato.princeton.edu. Retrieved 4 November 2023.
  62. ^ Steinhardt, P. J.; Alben, R.; Duffy, M. G.; Polk, D. E. (1973). "Relaxed Continuous Random Network Models". Phys. Rev. B. 8 (12): 6021–6023. Bibcode:1973PhRvB...8.6021S. doi:10.1103/physrevb.8.6021.
  63. ^ Alben, R.; Weaire, D.; Steinhardt, P.J. (1973). "One Band Density of States for the Polk Model". Journal of Physics. 6 (20): L384–L386. Bibcode:1973JPhC....6L.384A. doi:10.1088/0022-3719/6/20/003.
  64. ^ "APS Fellow Archive". www.aps.org. Retrieved 28 January 2019.
  65. ^ "Guggenheim Foundation Fellow". Retrieved 15 September 2019.
  66. ^ "Paul Steinhardt". www.nasonline.org. Retrieved 28 January 2019.
  67. ^ "2018 Stanley Corrsin Award Recipient". www.aps.org. Retrieved 28 January 2019.
  68. ^ "John Scott Award Recipients 2001-2011". www.garfield.library.upenn.edu. Retrieved 28 January 2019.
  69. ^ . Archived from the original on 2015-01-06. Retrieved 2015-01-06.
  70. ^ "Paul Steinhardt". Radcliffe Institute for Advanced Study at Harvard University. 7 May 2012. Retrieved 28 January 2019.
  71. ^ "Distinguished Alumni Awards". Caltech Alumni Association. Retrieved 28 January 2019.
  72. ^ "Aspen Institute Italia Award".
  73. ^ "Niels Bohr Institute, Receivers of the Medal of Honour". 9 August 2013.

January 01, 1970
paul, steinhardt, paul, joseph, steinhardt, born, december, 1952, american, theoretical, physicist, whose, principal, research, cosmology, condensed, matter, physics, currently, albert, einstein, professor, science, princeton, university, where, faculty, both,. Paul Joseph Steinhardt born December 25 1952 is an American theoretical physicist whose principal research is in cosmology and condensed matter physics He is currently the Albert Einstein Professor in Science at Princeton University where he is on the faculty of both the Departments of Physics and of Astrophysical Sciences 3 Paul SteinhardtBornPaul Joseph Steinhardt 1952 12 25 December 25 1952 age 71 Washington D C USAlma materCaltech B S Harvard University M A Ph D Known forCosmic inflation Eternal inflation Cyclic model Ekpyrotic universe Quintessence Self interacting dark matter Quasicrystals IcosahedriteAwardsGuggenheim Fellowship 1994 Dirac Medal 2002 Oliver E Buckley Condensed Matter Prize 2010 John Scott Award 2012 Simons Fellow 2012 Radcliffe Fellow 2012 Niels Bohr Institute Medal of Honour 2020 Scientific careerFieldsTheoretical physicsCosmologyCondensed Matter PhysicsInstitutionsPrinceton University University of Pennsylvania Harvard University CaltechThesisLattice theory of SU N flavor quantum electrodynamics in 1 1 dimensions 1978 Doctoral advisorSidney R Coleman 1 Other academic advisorsRichard P Feynman Barry Barish Frank Sciulli Richard Alben Praveen ChaudhariDoctoral studentsAndreas Albrecht 1 Dov Levine Katie Mack 2 Websitepaulsteinhardt wbr org Steinhardt is best known for his development of new theories of the origin evolution and future of the universe He is also well known for his exploration of a new form of matter known as quasicrystals which were thought to exist only as man made materials until he co discovered the first known natural quasicrystal in a museum sample 4 He subsequently led a separate team that followed up that discovery with several more examples of natural quasicrystals recovered from the wilds of the Kamchatka Peninsula in far eastern Russia Several years later he and collaborators reported the accidental synthesis of a previously unknown type of quasicrystal in the remnants of the first atomic bomb test on July 16 1945 at Alamagordo New Mexico 5 He has written two popular books on these topics Endless Universe Beyond the Big Bang 2007 co authored with Neil Turok describes the early struggles in challenging the widely accepted big bang theory and the subsequent development of the bouncing or cyclic theories of the universe which are currently being explored and tested 6 The Second Kind of Impossible The Extraordinary Quest for a New Form of Matter 2019 recounts the story of quasicrystals from his invention of the concept with his then student Dov Levine to his expedition to far eastern Russia to recover meteorite fragments containing natural quasicrystal grains formed billions of years ago 7 Contents 1 Education and career 2 Research 2 1 Inflationary cosmology 2 2 Bouncing and cyclic cosmology 2 3 Dark energy and dark matter 2 4 Quasicrystals 2 5 Photonics and hyperuniformity 2 6 Amorphous solids 3 Honors and awards 4 ReferencesEducation and career editBorn in 1952 to Helen and Charles Steinhardt Paul Steinhardt is the second oldest of four children He grew up in Miami Florida where he attended Coral Gables Senior High School while attending classes at a local university Steinhardt received his Bachelor of Science in Physics at Caltech in 1974 and his Ph D in Physics at Harvard University in 1978 where his advisor was Sidney Coleman 1 He was a Junior Fellow in the Harvard Society of Fellows from 1978 to 1981 rose from junior faculty to Mary Amanda Wood Professor at the University of Pennsylvania between 1981 and 1998 during which he maintained a long term association with the Thomas J Watson Research Center and has been on the faculty at Princeton University since the Fall of 1998 He co founded the Princeton Center for Theoretical Science and served as its Director from 2007 to 2019 8 Research editInflationary cosmology edit Beginning in the early 1980s Steinhardt co authored seminal papers that helped to lay the foundations of inflationary cosmology nbsp Steinhardt at University of Pennsylvania Slow roll inflation and Generation of the seeds for galaxies In 1982 Steinhardt and Andreas Albrecht 9 and independently Andrei Linde constructed the first inflationary models that could speed up the expansion of the universe enough to explain the observed smoothness and flatness of the universe and then gracefully exit to the more modest expansion observed today 10 The Albrecht Steinhardt paper was the first to note the effect of Hubble friction in sustaining inflation for a sufficiently long period the slow roll effect setting the prototype for most subsequent inflationary models Hubble friction played a critical role in the 1983 paper by James Bardeen Steinhardt and Michael S Turner 11 who were the first to introduce a reliable relativistically gauge invariant method to compute how quantum fluctuations during inflation might naturally generate a nearly scale invariant spectrum of density fluctuations with a small tilt properties later shown by observations of the cosmic microwave background to be features of our universe The density fluctuations are seeds about which galaxies eventually form Contemporaneous calculations by several other groups obtained similar conclusions using less rigorous methods Eternal inflation and the multiverse In 1982 Steinhardt presented the first example of eternal inflation 12 Neverending inflation was eventually shown to be a generic feature of inflationary models that leads to a multiverse the break up of space into an infinite multitude of patches spanning an infinite range of outcomes instead of the single smooth and flat universe as originally hoped when first proposed Although some cosmologists would later come to embrace the multiverse Steinhardt consistently expressed his concern that it utterly destroys the predictive power of the theory he helped create Because the inflationary theory leads to a multiverse that allows for every possible outcome Steinhardt argued we must conclude that the inflationary theory actually predicts nothing 13 14 15 Imprint of gravitational waves on the cosmic microwave background In 1993 Robert Crittenden Rick Davis J R Bond G Efstathiou and Steinhardt performed the first calculations of the complete imprint of gravitational waves on the B mode temperature maps and on the polarization of the microwave background radiation in 1993 16 17 Despite his criticisms of the idea Steinhardt s major contributions to the inflationary theory were recognized in 2002 when he shared the Dirac Prize with Alan Guth of M I T and Andrei Linde of Stanford 18 The unlikeliness problem In 2013 Anna Ijjas Abraham Loeb and Steinhardt added to the criticisms in a widely discussed pair of papers that the inflationary model was much less likely to explain our universe than previously thought 19 20 According to their analysis of the Planck satellite 2013 results the chances of obtaining a universe matching the observations after a period of inflation is less than one in a googolplex 21 Steinhardt and his team dubbed the result the unlikeliness problem The two papers also showed that Planck satellite data ruled out what had been historically accepted as the simplest inflationary models and that the remaining inflationary models require more parameters more fine tuning of those parameters and more unlikely initial conditions 19 20 In 2015 the unlikeness problem was reaffirmed and strengthened by a subsequent round of measurements reported by the Planck satellite team Incompatibility with the string swampland conjectures In 2018 Steinhardt in collaboration with Prateek Agrawal George Obieds and Cumrun Vafa argued that inflation may also be incompatible with string theory because inflationary models generally violate constraints sometimes called the swampland conjectures on what is required for a model to be consistent with quantum gravity 22 Bouncing and cyclic cosmology edit Motivated by what he viewed as the failures of inflationary theory including but not limited to the multiverse Steinhardt became a leading developer of a new class of cosmological models that replace the so called big bang with a bounce and replace inflation with a period of slow contraction preceding the bounce The hypothetical idea that the universe began with a bang is based on extrapolating back in time assuming that Einstein s equations of general relativity remain valid at energies and temperatures far greater than have ever been tested Theorists generally agree that if there was a big bang then in the instants following quantum physics effects should have created large fluctuations in spacetime These fluctuations would have caused space time to curve and warp and the distribution of energy to become very uneven all of which is inconsistent with what experimentalists observe when they study the early universe The universe is in fact observed to be homogeneous 23 Inflation was originally invented to expain the smoothness that is observed in the universe But it is unclear how to transition from the highy uneven conditions created after a big bang to an inflationary universe and even if a solution could be found the inflationary theory ultimately results in a multiverse rather than a smooth universe 15 The new approach removes the bang altogether envisioning instead a smooth transition from a previous period of slow contraction to the current period of expansion If the contraction is slow it smooths the entire universe and unlike inflation there is no multiverse By evading the infamous cosmic singularity problem associated with a big bang a bounce avoids quantum gravity effects that produce an unsmooth universe A natural extension of these ideas is a never beginning and never ending cyclic universe in which epochs of bounce expansion and contraction repeat at regular intervals In a pivotal lecture in 2021 Steinhardt explained why it is time to jettison the big bang theory and replace the bang with a bounce a smooth transition from contraction to a dense hot universe that continues to expand and cool 24 Historical DevelopmentEarly models with a big crunch In 2001 Steinhardt presented the first examples of these bouncing and cyclic models referred to as ekpyrotic in papers with Justin Khoury Burt A Ovrut and Neil Turok 25 These models were based on the speculative notion suggested by string theory that the universe has extra dimensions bounded by branes where brane is derived from membrane a basic object in string theory The fiery collision and rebound of these branes is comarable to a big crunch a violent event that would depend sensitively on strong quantum gravity effects that are not yet established and may create tremendous curvature and warping of spacetime In principle the collisions can repeat at regular intervals resulting in a cyclic universe 15 In 2002 Steinhardt and Turok incorporated the ekpyrotic idea into an early version of a cyclic theory of the universe 26 Improved models with slow contraction and a gentle bounce Recent versions of bouncing cosmology developed by Anna Ijjas and Steinhardt introduce elements that simplify and address problems with the earlier ekpyrotic proposal They do not require extra dimensions or branes or string theory ordinary fields with potential energy evolving in space time similar to inflationary models can be used 27 Instead of a violent ekpyrosis the collision of two branes the smoothing and flattening of spacetime occurs through slow contraction a period in which space contracts very little while the Hubble radius contracts a lot By the time the bounce is reached the universe is supersmoothed 28 The bounce is a gentle transition that can be fully computed and maintains smoothness because it is a continuoous process that occurs long before quantum gravity effects become strong There is no cosmic singularity problem unlike theories based on the big bang Universal smoothing and ultralocality To test these ideas Anna Ijjas adapted the tools of numerical general relativity originally invented to simulate the merger of black holes and the emission of gravitational waves to cosmology Together with Steinhardt and collaborators the new tools were used to study the effectiveness of slow contraction 28 29 30 The study demonstrates that slow contraction is a supersmoothing cosmological phase that homogenizes isotropizes and flattens the universe both classically and quantum mechanically and can do so far more robustly and rapidly than had been realized in earlier studies Beginning from wildly unsmooth and curvy starting condition the studies verified that slow contraction smooths virtually all of spacetime due to an effect of general relativity known as ultralocality 31 The ultralocal effect is specific to a contracting universe and there is no equivalent in an expanding universe including the case of inflation The consequent smoothing power is an unparalleled advantage of slow contraction Cyclic version of bouncing cosmology In the cyclic version of these models space never crunches rather it necessarily grows by a constant factor overall from bounce to bounce every 100 billion years or so After each bounce gravitational energy is converted into the matter and radiation that fuels the next cycle To an observer the evolution appears to be cyclic because the temperature density number of stars and galaxies etc are on average the same from one cyclic to the next and the observer cannot see far enough to know that there is the observer cannot see far enough to know that there is an ever increasing amount of space matter energy outside the horizon The fact that the universe expands overall from cycle to cycle means that the entropy produced in earlier cycles by the formation of stars and other entropy producing processes is increasingly diluted as the cycles proceed and so does not have any physical effect on cosmic evolution 27 This growth from cycle to cycle and associated entropy dilution are features that distinguish these new cyclic models from versions discussed in the 1920s by Friedmann and Tolman and explain how the new cyclic model avoids the entropy problem that beset earlier versions Theoretical advantages of the new cyclic modelThe new cyclic models have two important advantages over inflationary models First because they do not include inflation they do not produce a multiverse As a result unlike inflation cyclic models produce a single universe that everywhere have the same predicted properties that are subject to empirical tests Second cyclic models explain why there must be dark energy According to these models the accelerated expansion caused by dark energy starts the smoothing process the decay of dark energy to other forms of energy starts a period of slow contraction and the slow contraction is what is responsible for smoothing and flattening the universe 27 Theoretical predictions of the new cyclic modelOne prediction of the cyclic models is that unlike inflation no detectable gravitational waves are generated during the smoothing and flattening process The Simons Observatory being built in the Atacama Desert in Chile will test this prediction Instead the prediction of the cyclic models is that the only source of gravitational waves on cosmic wavelength scales are so called secondary gravitational waves that are produced long after the bounce Their amplitudes are far too weak to be found in current detectors but are ultimately detectable A second prediction is that the current acceleration expansion must eventually stop and the vacuum must be eventually decay in order to initiate the next cycle 27 Other predictions depend on the specific fields or branes that cause the contraction Observational support for the new cyclic modelThe cyclic model may naturally explain why the cosmological constant is exponentially small and positive compared to the enormous value expected by quantum gravity theories 32 The cosmological constant might begin large as expected but then might slowly decay over the course of many cycles to the tiny value observed today The discovery of the Higgs field at the Large Hadron Collider LHC may provide added support for the cyclic model 33 Evidence from the LHC suggests that the current vacuum may decay in the future according to calculations made by Steinhardt Turok and Itzhak Bars The decay of the current vacuum is required by the cyclic model in order to end the current phase of expansion contract bounce and begin a new era of expansion the Higgs provides a possible mechanism of decay that can be tested The Higgs field is a viable candidate for the field that drives the cycles of expansion and contraction and this may ultimately be testable Dark energy and dark matter edit Steinhardt has made significant contributions researching the dark side of the universe dark energy the cosmological constant problem and dark matter First evidence of cosmic acceleration In 1995 Steinhardt and Jeremiah Ostriker used a concordance of cosmological observations to show there must be a non zero dark energy component today more than 65 percent of the total energy density sufficient to cause the expansion of the universe to accelerate 34 This was verified three years later by supernova observations in 1998 35 36 37 Quintessence Working with colleagues he subsequently introduced the concept of quintessence a form of dark energy that varies with time 38 It was first posited by Steinhardt s team as an alternative to the cosmological constant which is by definition constant and static quintessence is dynamic Its energy density and pressure evolve over time The 2018 paper on swampland conjectures with Agrawal Obieds and Vafa 22 points to quintessence as being the only option for dark energy in string theory and consistent quantum gravity Self interacting dark matter In 2000 David Spergel and Steinhardt first introduced the concept of strongly self interacting dark matter SIDM to explain various anomalies in standard cold dark models based on assuming dark matter consists of weakly interacting massive particles also referred to as WIMPs 39 In 2014 Steinhardt Spergel and Jason Pollack have proposed that a small fraction of dark matter could have ultra strong self interactions which would cause the particles to coalesce rapidly and collapse into seeds for early supermassive black holes 40 Quasicrystals edit Development of the theory In 1983 Steinhardt and his then student Dov Levine first introduced the theoretical concept of quasicrystals in a patent disclosure 7 The complete theory was published the following year in a paper entitled Quasicrystals A New Class of Ordered Structures 41 The theory proposed the existence of a new phase of solid matter analogous to Penrose tilings with rotational symmetries previously thought to be impossible for solids Steinhardt and Levine named the new phase of matter a quasicrystal The never before seen atomic structure had quasiperiodic atomic ordering rather than the periodic ordering characteristic of conventional crystals The new theory overturned 200 years of scientific dogma and proved that quasicrystals could violate all of the previously accepted mathematical theorems about the symmetry of matter Symmetries once thought to be forbidden for solids are actually possible for quasicrystals including solids with axes of five fold symmetry and three dimensional icosahedral symmetry The first reported example of a synthetic quasicrystal Working simultaneously to but independently of Steinhardt and Levine Dan Shechtman Ilan Blech Denis Gratias and John Cahn at the National Bureau of Standards NBS were focused on an experimental discovery they could not explain It was an unusual alloy of manganese and aluminum with a diffraction pattern of what appeared to be sharp though not perfectly point like spots arranged with icosahedral symmetry that did not fit any known crystal structure 42 The alloy was first noted in 1982 but results were not published until November 1984 after more convincing data had been obtained 7 Steinhardt and Levine were shown a preprint of the Shechtman team s paper and immediately recognized that it could be experimental proof of their still unpublished quasicrystal theory 7 The theory along with the proposal that it could explain the mysterious forbidden structure of the new alloy was published in December 1984 41 The new alloy was ultimately discovered to be problematic It proved to be unstable and the noted imperfections in the diffraction pattern allowed for multiple explanations including one about crystal twinning proposed by Linus Pauling that were hotly debated for the next few years 7 In 1987 An Pang Tsai and his group at Japan s Tohoku University made an important breakthrough with the synthesis of the first ever stable icosahedral quasicrystal It had sharp diffraction spots arranged in close accord with Steinhardt and Levine s quasicrystal theory and was inconsistent with any of the alternative explanations 43 The theoretical debate was effectively ended and the Steinhardt Levine theory gained wide acceptance 7 nbsp Small sample about 3 mm across of a Khatyrkite bearing meteorite top and bottom left panels from the mineral collection at the Museo di Storia Naturale in Florence Italy On January 2 2009 Paul Steinhardt and Nan Yao identified the first known natural quasicrystal embedded in the sample area of discovery indicated by red circle in bottom right panel The first natural quasicrystal In 1999 Steinhardt assembled a team at Princeton University to search for a natural quasicrystal The team composed of Peter Lu Ken Deffeyes and Nan Yao devised a novel mathematical algorithm to search through an international database of powder diffraction patterns 7 44 For the first eight years the search yielded no results In 2007 Italian scientist Luca Bindi then curator of the mineral collection at the Universite di Firenze joined the team 7 Two years later Bindi identified a promising specimen in his museum s storage room 4 The tiny specimen a few millimeters across had been packed away in a box labeled khatyrkite which is an ordinary crystal composed of copper and aluminum On January 2 2009 Steinhardt and Nan Yao director of the Princeton Imaging Center examined the material and identified the signature diffraction pattern of an icosahedral quasicrystal This was the first known natural quasicrystal 4 nbsp The electron diffraction pattern for icosahedrite the first natural quasicrystal obtained by aiming the electron beam down a fivefold axis of symmetry The patterns correspond perfectly up to experimental resolution with the fivefold patterns first predicted by Paul Steinhardt and Dov Levine in the 1980s for an icosahedral quasicrystal The International Mineralogical Association accepted the quasicrystal as a new mineral and designated its name icosahedrite 4 The material had exactly the same atomic composition Al63Cu24Fe13 as the first thermodynamically stable quasicrystal synthesized by An Pang Tsai and his group in their laboratory in 1987 Expedition to Chukotka Two years after identifying the museum sample Steinhardt organized an international team of experts and led them on an expedition to its source the remote Listventovyi stream in the Chukotka Autonomous Okrug in the northern half of the Kamchatka Peninsula in far eastern Russia The team included Bindi and Valery Kryachko the Russian ore geologist who had found the original samples of khatyrkite crystal while working at the Listventovyi stream in 1979 7 nbsp On location at the Listventovyi stream in the Kamchatka Peninsula in 2011 left to right Luca Bindi University of Firenze Italy Valery Kryachko IGEM Russia and Paul Steinhardt Princeton USA Other members of the team were Chris Andronicos Vadim Distler Michael Eddy Alexander Kostin Glenn MacPherson Marina Yudovskaya and Steinhardt s son William Steinhardt 7 After digging and panning a ton and a half of clay along the banks of the Listvenitovyi stream in the Koryak Mountains eight different grains containing icosahedrite were identified 7 During subsequent years of study Steinhardt s team proved that both the sample found in the Florence museum and the samples recovered from the field in Chukotka originated from a meteorite formed 4 5 billion years ago before there were planets and landed on the Earth about 15 000 years ago 45 More natural quasicrystals Further studies revealed other new minerals in the Chukotka samples In 2014 one of those minerals was discovered to be a crystalline phase of aluminum nickel and iron Al38Ni33Fe30 It was accepted by the International Mineralogical Association and named steinhardtite in Steinhardt s honor 46 In 2015 a second type of natural quasicrystal was discovered in a different grain of the same meteorite The second known natural quasicrystal was found to be a different mixture of aluminum nickel and iron Al71Ni24Fe5 and had a decagonal symmetry a regularly stacking of atomic layers which each have 10 fold symmetry It was accepted by the International Mineralogical Association and given the name decagonite 47 48 Three more crystalline minerals were also discovered and named after colleagues involved in Steinhardt s quasicrystal research hollisterite for Princeton petrologist Lincoln Hollister kryachkoite for Russian geologist Valery Kryachko and stolperite for Caltech s former provost Ed Stolper 7 nbsp Girih tile quasicrystal pattern on right half of spandrel at Darb e Imam Shrine A previously unknown quasicrystal created by the first atomic bomb test In 2021 Steinhardt led the team that discovered a novel icosahedral quasicrystal created by the detonation of the first nuclear device at Alamogordo New Mexico on July 16 1945 the Trinity test The new quasicrystal was discovered within a sample of red trinitite and is the oldest extant anthropogenic quasicrystal ever discovered 5 The previously unknown structure which is made of iron silicon copper and calcium is thought to have been formed by the fusion of vaporized desert sand and copper cables during the atomic test blast 49 The discovery of a unique quasicrystal in trinitite could transform the field of nuclear forensics leading to a new diagnostic tool 50 which could help law enforcement prevent future terrorist attacks by using quasicrystals which unlike radioactive debris and gases do not decay to identify the signature of an atomic weapon and track down the culprits 51 Other contributions to the field Steinhardt and his collaborators have made significant contributions to understanding the quasicrystals unique mathematical and physical properties 52 including theories of how and why quasicrystals form 53 and their elastic and hydrodynamics properties 54 Peter J Lu and Steinhardt discovered a quasicrystalline Islamic tiling on the Darb e Imam Shrine 1453 A D in Isfahan Iran constructed from girih tiles 55 In 2007 they deciphered the manner in which early artists created increasingly complex periodic girih patterns Those early designs were shown to have culminated in the development of a nearly perfect quasi crystalline pattern five centuries before the discovery of Penrose patterns and the Steinhardt Levine quasicrystal theory 7 Photonics and hyperuniformity edit Steinhardt s research on quasicrystals and other non crystalline solids expanded into work on designer materials with novel photonic and phononic properties Photonic quasicrystals A team of researchers including Steinhardt Paul Chaikin Weining Man and Mischa Megens designed and tested the first photonic quasicrystal with icosahedral symmetry in 2005 They were the first to demonstrate the existence of photonic band gaps PBGs 56 These materials block light for a finite range of frequencies or colors and let pass light with frequencies outside that band similar to the way in which a semiconductor blocks electrons for a finite range of energies Hyperuniform disordered solids HUDS Working with Salvatore Torquato and Marian Florescu in 2009 Steinhardt discovered a new class of photonic materials called hyperuniform disordered solids HUDS and showed that solids consisting of a hyperuniform disordered arrangement of dielectric elements produce band gaps with perfect spherical symmetry 57 58 These materials which act as isotropic semiconductors for light can be used to control and manipulate light in a wide range of applications including optical communications photonic computers energy harvesting non linear optics and improved light sources Phoamtonics In 2019 Steinhardt along with Michael Klatt and Torquato introduced the idea of phoamtonics which refers to photonic materials based on foam like designs 59 They showed that large photonic bandgaps could arise in network structures created by converting the foam edges intersections between foam bubbles to a dielectric material for the two most famous crystalline foam structures Kelvin foams and Weiare Phelan foams Etaphase Inc The meta material breakthroughs by Steinhardt and his Princeton colleagues have valuable commercial applications In 2012 the scientists helped create a start up company called Etaphase which will apply their discoveries to a wide range of high performance products The inventions will be used in integrated circuits structural materials photonics communications chip to chip communications intra chip communications sensors datacomm networking and solar applications 60 61 Amorphous solids edit Steinhardt s research in disordered forms of matter has centered on the structure and properties of glasses and amorphous semiconductors and amorphous metals He constructed the first computer generated continuous random network CRN model of glass and amorphous silicon in 1973 while still an undergraduate at Caltech CRNs remain the leading model of amorphous silicon and other semiconductors today Working with Richard Alben and D Weaire he used the computer model to predict structural and electronic properties 62 63 Working with David Nelson and Marco Ronchetti Steinhardt formulated mathematical expressions known as orientational order parameters for computing the degree of alignment of interatomic bonds in liquids and solids in 1981 Applying them to computer simulations of monatomic supercooled liquids they showed that the atoms form arrangements with finite range icosahedral soccer ball like bond orientational order as liquids cool Honors and awards editIn 1986 Steinhardt was elected as a Fellow in the American Physical Society in recognition of his contributions to cosmology and to the theoretical understanding of quasicrystals 64 In 1994 he was named a Guggenheim Fellow 65 In 1998 he was elected to the United States National Academy of Sciences 66 In 2002 Steinhardt was honored for his work on the inflationary model of the universe with the P A M Dirac Medal from the International Centre for Theoretical Physics He shared the award with Alan Guth of MIT and Andrei Linde of Stanford 18 In 2010 Steinhardt received the Oliver E Buckley Condensed Matter Prize of the American Physical Society for his pioneering contributions to the theory of quasicrystals 67 In 2012 he received the John Scott Award for his work on quasicrystals 68 In 2012 Steinhardt was named Simons Fellow in Theoretical Physics 69 and Radcliffe Fellow at the Radcliffe Institute for Advanced Study at Harvard 70 In 2014 he received the Caltech Distinguished Alumni Award 71 In 2014 the International Mineralogical Association accepted a new mineral from the Khatyrka meteorite into the official catalogue of natural minerals and named it steinhardtite in his honor 46 In 2018 he shared the Aspen Institute Italia Award with Luca Bindi for scientific research and collaboration between Italy and the United States 72 In 2020 he received the Niels Bohr Institute Medal of Honour 73 References edit a b c Paul Steinhardt at the Mathematics Genealogy Project nbsp Mack Katherine J 2009 Tests of early universe physics from observational astronomy Thesis ProQuest 304982499 Biographical Sketch Prof Paul J Steinhardt Department of Physics at Princeton University Retrieved January 29 2019 a b c d Bindi L Steinhardt P J Yao N Lu P 2009 Natural Quasicrystals Science 324 5932 1306 1309 Bibcode 2009Sci 324 1306B doi 10 1126 science 1170827 PMID 19498165 S2CID 14512017 a b Bindi Luca Kolb William Eby G Nelson Asimow Paul D Wallace Terry C Steinhardt Paul J 2021 Accidental synthesis of a previously unknown quasicrystal in the first atomic bomb test PNAS 118 June 1 2021 118 22 e2101350118 e2101350118 Bibcode 2021PNAS 11801350B doi 10 1073 pnas 2101350118 PMC 8179242 PMID 34001665 Steinhardt P J Turok N G 2007 Endless Universe beyond the Big Bang Doubleday ISBN 9780385509640 a b c d e f g h i j k l m Steinhardt P J 2019 The Second Kind of Impossible Simon amp Schuster ISBN 9781476729923 Paul Steinhardt Bio Paul Steinhardt Retrieved 26 June 2019 Albrecht A Steinhardt P J 1982 Cosmology For Grand Unified Theories With Radiatively Induced Symmetry Breaking Phys Rev Lett 48 17 1220 1223 Bibcode 1982PhRvL 48 1220A doi 10 1103 PhysRevLett 48 1220 Albrecht A Steinhardt P J 1982 Reheating an Inflationary Universe Phys Rev Lett 48 20 1437 1440 Bibcode 1982PhRvL 48 1437A doi 10 1103 PhysRevLett 48 1437 Bardeen J M Steinhardt P J Turner M S 1983 Spontaneous Creation Of Almost Scale Free Density Perturbations In An Inflationary Universe Phys Rev D 28 4 679 693 Bibcode 1983PhRvD 28 679B doi 10 1103 PhysRevD 28 679 Gibbons Gary W Hawking Stephen W Siklos S T C eds 1983 Natural Inflation The Very Early Universe Cambridge University Press pp 251 66 ISBN 978 0 521 31677 4 Steinhardt Paul J April 2011 Inflation Debate Is the theory at the heart of modern cosmology deeply flawed PDF Scientific American 304 4 36 43 Bibcode 2011SciAm 304d 36S doi 10 1038 scientificamerican0411 36 PMID 21495480 Steinhardt Paul J The Cyclic Theory of the Universe PDF www prsinstitute org Retrieved 4 November 2023 a b c Horgan John December 1 2014 Physicist Slams Cosmic Theory He Helped Conceive Scientific American Crittenden R Bond J R Davis R L Efstathiou G E Steinhardt P J 1993 The Imprint of Gravitational Waves on the Cosmic Microwave Background Phys Rev Lett 71 3 324 327 arXiv astro ph 9303014 Bibcode 1993PhRvL 71 324C doi 10 1103 PhysRevLett 71 324 PMID 10055242 S2CID 18553924 Crittenden Davis R L Steinhardt P J 1993 Polarization of the Microwave Background due to Primordial Gravitational Waves Astrophysical Journal Letters 417 L13 L16 arXiv astro ph 9306027 Bibcode 1993ApJ 417L 13C doi 10 1086 187082 S2CID 18194291 a b ICTP International Centre for Theoretical Physics www ictp it Retrieved 28 January 2019 a b Iijas Anna Loeb Abraham Steinhardt Paul 2013 Inflationary Paradigm in trouble after Planck 2013 Phys Lett B 723 4 5 261 266 arXiv 1304 2785 Bibcode 2013PhLB 723 261I doi 10 1016 j physletb 2013 05 023 S2CID 14875751 a b Iijas Anna Steinhardt Paul J Loeb Abraham 2014 Inflationary Schism Phys Lett B 7 142 146 arXiv 1402 6980 Bibcode 2014PhLB 736 142I doi 10 1016 j physletb 2014 07 012 S2CID 119096427 Filling the Big Gap in Einstein s Theory Paul Steinhardt TEDxCLESalon YouTube Retrieved September 21 2016 a b Obied Georges Ooguri Hirosi Steinhardt Paul J 2018 On the Cosmological Implications of the String Swampland Phys Lett B 784 271 276 arXiv 1806 09718 Bibcode 2018PhLB 784 271A doi 10 1016 j physletb 2018 07 040 S2CID 119252887 Planck reveals an almost perfect Universe ESA Retrieved January 21 2024 Paul Steinhardt Time to Take the Big Bang out of the Big Bang Theory YouTube Retrieved January 21 2024 Khoury J Ovrut B Steinhardt P J 2001 The Ekpyrotic Universe Colliding Branes and the Origin of the Hot Big Bang Phys Rev D 64 12 123522 arXiv hep th 0103239 Bibcode 2001PhRvD 64l3522K doi 10 1103 PhysRevD 64 123522 S2CID 374628 Steinhardt P J Turok N 2002 04 25 A Cyclic Model of the Universe Science 296 5572 1436 1439 arXiv hep th 0111030 Bibcode 2002Sci 296 1436S doi 10 1126 science 1070462 PMID 11976408 S2CID 1346107 a b c d Ijjas Anna Steinhardt Paul J 2019 A new kind of cyclic universe Phys Lett B 795 666 672 arXiv 1904 08022 Bibcode 2019PhLB 795 666I doi 10 1016 j physletb 2019 06 056 S2CID 118712442 a b Cook William G Glushchenko Iryna A Ijjas Anna Pretorius Franz Steinhardt Paul J 2020 Supersmoothing through Slow Contraction Phys Lett B 808 arXiv 2006 01172 doi 10 1016 j physletb 2020 135690 Ijjas Anna Cook William G Pretorius Franz Steinhardt Paul J Davies Elliot Y 2020 Robustness of slow contraction to cosmic initial conditions JCAP 2020 arXiv 2006 04999v2 doi 10 1088 1475 7516 2020 08 030 Garfinkle David Ijjas Anna Steinhardt Paul J 2023 Initial conditions problem in cosmological inflation revisited Phys Lett B 843 arXiv 2304 12150 doi 10 1016 j physletb 2023 13802 Ijjas Anna Sullivan Andrew P Pretorius Frans Steinhardt Paul J Cook William G 2021 Ultralocality and Slow Contraction JCAP 2021 arXiv 2103 00584v1 doi 10 1088 1475 7516 2021 06 013 Steinhardt P J Turok N 2006 Why the cosmological constant is small and positive Science 312 5777 1180 1182 arXiv astro ph 0605173 Bibcode 2006Sci 312 1180S doi 10 1126 science 1126231 PMID 16675662 S2CID 14178620 Bars I Steinhardt P J Turok N 2013 Cyclic cosmology conformal symmetry and the metastability of the Higgs Phys Lett B 726 1 3 50 55 arXiv 1307 8106 Bibcode 2013PhLB 726 50B doi 10 1016 j physletb 2013 08 071 S2CID 592287 Ostriker J P Steinhardt P J 1995 The observational case for a low density Universe with a non zero cosmological constant Nature 377 6550 600 602 Bibcode 1995Natur 377 600O doi 10 1038 377600a0 S2CID 4236645 Riess A al et 1998 Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant The Astronomical Journal 116 3 1009 1038 arXiv astro ph 9805201 Bibcode 1998AJ 116 1009R doi 10 1086 300499 S2CID 15640044 Perlmutter S al et 1999 Measurements of Omega and Lamba from 42 High Redshift Supernovae The Astrophysical Journal 517 2 565 586 arXiv astro ph 9812133 Bibcode 1999ApJ 517 565P doi 10 1086 307221 S2CID 118910636 Bahcall N A Ostriker J P Perlmutter S Steinhardt P J 1999 The Cosmic Triangle Revealing the State of the Universe Science 284 5419 1481 1488 arXiv astro ph 9906463 Bibcode 1999Sci 284 1481B doi 10 1126 science 284 5419 1481 S2CID 15271568 Caldwell R R Dave R Steinhardt P J 1998 Cosmological Imprint of an Energy Component with General Equation of State Phys Rev Lett 80 8 1582 1585 arXiv astro ph 9708069 Bibcode 1998PhRvL 80 1582C doi 10 1103 PhysRevLett 80 1582 S2CID 597168 Spergel D N Steinhardt P J 2000 Observational Evidence for Self Interacting Cold Dark Matter Phys Rev Lett 84 17 3760 3763 arXiv astro ph 9909386 Bibcode 2000PhRvL 84 3760S doi 10 1103 PhysRevLett 84 3760 PMID 11019199 S2CID 6669358 Pollack Jason Spergel David N Steinhardt Paul J 2014 Supermassive Black Holes from Ultra Strongly Self Interacting Dark Matter The Astrophysical Journal 804 2 131 arXiv 1501 00017 Bibcode 2015ApJ 804 131P doi 10 1088 0004 637X 804 2 131 S2CID 15916893 a b Levine D Steinhardt P J 1984 Quasicrystals A New Class of Ordered Structures PDF Phys Rev Lett 53 26 2477 2480 Bibcode 1984PhRvL 53 2477L doi 10 1103 PhysRevLett 53 2477 Shechtman D Blech I Gratias D Cahn J W 1984 Metallic Phase with Long Range Orientational Order and No Translational Symmetry Phys Rev Lett 53 20 1951 1953 Bibcode 1984PhRvL 53 1951S doi 10 1103 PhysRevLett 53 1951 Tsai An Pang Inoue Akihisa Masumoto Tsuyoshi 1987 A Stable Quasicrystal in Al Cu Fe System Japanese Journal of Applied Physics 26 Part 2 Number 9 L1505 L1507 Bibcode 1987JaJAP 26L1505T doi 10 1143 JJAP 26 L1505 S2CID 98442801 Lu P Deffreyes K Steinhardt P J Yao 2001 Identifying and Indexing Icosahedral Quasicrystals from Powder Diffraction Patterns Phys Rev Lett 87 27 275507 arXiv cond mat 0108259 Bibcode 2001PhRvL 87A5507L doi 10 1103 PhysRevLett 87 275507 PMID 11800896 S2CID 2814118 Wolchover Natalie 13 June 2014 In a grain a Glimpse of the Cosmos Quanta Magazine Retrieved October 11 2015 a b Williams Professor Peter July 1 2014 Letter to Luca Bindi PDF School of Science and Health Western Sydney University Paul J Steinhardt Retrieved January 29 2019 Bindi Luca Yao Nan Lin Chaney Hollister Lincoln S Andronicos Christopher L Distler Vadim V Eddy Michael P Kostin Alexander Kryachko Valery MacPherson Glenn J Steinhardt William M Yudovskaya Marina Steinhardt Paul J 2015 Natural quasicrystal with decagonal symmetry Scientific Reports 5 9111 Bibcode 2015NatSR 5E9111B doi 10 1038 srep09111 PMC 4357871 PMID 25765857 Decagonite Al71Ni24Fe5 a quasicrystal with decagonal symmetry American Mineralogist 100 10 October 2015 doi 10 2138 am 2015 5423 S2CID 101528286 Castelvecchi Davide 2021 First nuclear detonation created impossible quasicrystals Nature 593 7860 487 Bibcode 2021Natur 593 487C doi 10 1038 d41586 021 01332 0 PMID 34007024 S2CID 234779438 D Agostino Susan 9 June 2021 What are atomic bomb quasicrystals and why do they matter Bulletin of the Atomic Scientists Retrieved June 13 2021 Sloan Marisa The First Atomic Bomb Created This Forbidden Quasicrystal Discover Magazine Retrieved July 25 2021 Socolar J Steinhardt P J 1986 Quasicrystals II Unit Cell Configurations PDF Phys Rev B 34 2 617 647 Bibcode 1986PhRvB 34 617S doi 10 1103 PhysRevB 34 617 PMID 9939668 Jeong H C Steinhardt P J 1996 A simpler approach to Penrose tiling with implications for quasicrystal formation Nature 382 6590 431 433 Bibcode 1996Natur 382 431S doi 10 1038 382431a0 S2CID 4354819 Levine D Lubensky T Ostlund S Ramaswamy S Steinhardt P J Toner J 1985 Elasticity and Dislocations in Pentagonal and Icosahedral Quasicrystals Phys Rev Lett 54 14 1520 1523 Bibcode 1985PhRvL 54 1520L doi 10 1103 PhysRevLett 54 1520 PMID 10031060 Lu P Steinhardt P J 2007 Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture Science 315 5815 1106 1110 Bibcode 2007Sci 315 1106L doi 10 1126 science 1135491 PMID 17322056 S2CID 10374218 Man W Megens M Steinhardt P J Chaikin P 2005 Experimental Measurement of the Photonic Properties of Icosahedral Quasicrystals Nature 436 7053 993 996 Bibcode 2005Natur 436 993M doi 10 1038 nature03977 PMID 16107842 S2CID 4408304 Florescu M Torquato S Steinhardt Paul J 2009 Designer disordered materials with large complete photonic band gaps Proceedings of the National Academy of Sciences 106 49 20658 20663 arXiv 1007 3554 Bibcode 2009PNAS 10620658F doi 10 1073 pnas 0907744106 PMC 2777962 PMID 19918087 Man W al et 2013 Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids Proceedings of the National Academy of Sciences 110 40 15886 15891 arXiv 1311 2632 Bibcode 2013PNAS 11015886M doi 10 1073 pnas 1307879110 PMC 3791749 PMID 24043795 Klatt Michael A Torquato Salvatore Steinhardt Paul J 2019 Phoamtonic designs yield sizeable 3D photonic band gaps Proceedings of the National Academy of Sciences 116 47 23480 23486 Bibcode 2019PNAS 11623480K doi 10 1073 pnas 1912730116 PMC 6876150 PMID 31694882 Etaphase Incorporated Etaphase Incorporated Retrieved 28 January 2019 Advancing photonic functionalities PDF torquato princeton edu Retrieved 4 November 2023 Steinhardt P J Alben R Duffy M G Polk D E 1973 Relaxed Continuous Random Network Models Phys Rev B 8 12 6021 6023 Bibcode 1973PhRvB 8 6021S doi 10 1103 physrevb 8 6021 Alben R Weaire D Steinhardt P J 1973 One Band Density of States for the Polk Model Journal of Physics 6 20 L384 L386 Bibcode 1973JPhC 6L 384A doi 10 1088 0022 3719 6 20 003 APS Fellow Archive www aps org Retrieved 28 January 2019 Guggenheim Foundation Fellow Retrieved 15 September 2019 Paul Steinhardt www nasonline org Retrieved 28 January 2019 2018 Stanley Corrsin Award Recipient www aps org Retrieved 28 January 2019 John Scott Award Recipients 2001 2011 www garfield library upenn edu Retrieved 28 January 2019 2012 Simons Fellows Awardees Theoretical Physics Simons Foundation Archived from the original on 2015 01 06 Retrieved 2015 01 06 Paul Steinhardt Radcliffe Institute for Advanced Study at Harvard University 7 May 2012 Retrieved 28 January 2019 Distinguished Alumni Awards Caltech Alumni Association Retrieved 28 January 2019 Aspen Institute Italia Award Niels Bohr Institute Receivers of the Medal of Honour 9 August 2013 Retrieved from https en wikipedia org w index php title Paul Steinhardt amp oldid 1212508111, 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.