Inflationary cosmology Beginning in the early 1980s, Steinhardt co-authored seminal papers that helped to lay the foundations of
inflationary cosmology.
Slow-roll inflation and generation of the seeds for galaxies In 1982, Steinhardt and
Andreas Albrecht (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. 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 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. 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. 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. 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. 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. 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. 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.
Bouncing and cyclic cosmology 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. Inflation was originally invented to explain the smoothness that is observed in the universe. But it is unclear how to transition from the highly 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.
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. 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 comparable 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.
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. 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." The bounce is a gentle transition that can be fully computed and maintains smoothness because it is a continuous 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. 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. 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 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. 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. 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 Steinhardt has made significant contributions researching the "dark side" of the universe:
dark energy, the
cosmological constant problem and
dark matter. 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. This was verified three years later by supernova observations in 1998. Working with colleagues, he subsequently introduced the concept of
quintessence, a form of dark energy that varies with time. 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 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.
Quasicrystals Development of the theory In 1983, Steinhardt and his then-student Dov Levine first introduced the theoretical concept of
quasicrystals in a patent disclosure. 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. The alloy was first noted in 1982, but results were not published until November 1984 after more convincing data had been obtained. The theoretical debate was effectively ended and the Steinhardt-Levine theory gained wide acceptance. 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. 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.
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 (). It was accepted by the International Mineralogical Association and named "steinhardtite" in Steinhardt's honor 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 () 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." 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. The discovery of a unique quasicrystal in trinitite could transform the field of
nuclear forensics, leading to a new diagnostic tool 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.
Other contributions to the field Steinhardt and his collaborators have made significant contributions to understanding the quasicrystals' unique mathematical and physical properties, including theories of how and why quasicrystals form and their elastic and
hydrodynamics properties.
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. 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. 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. 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. 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.
Amorphous solids 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. 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==