My research span problems in cosmology, astrophysics, particle
physics and condensed matter physics. In cosmology, my work has focused
on issues at the interface between
fundamental physics (particle physics and string theory), general relativity and astrophysics.
The mechanisms for driving inflationary expansion in the early universe,
the connection between inflation and elementary particles, and the observational
consequences of inflation are subjects of longstanding interest. In the last few years, my research has turned to a radical alternative to standard big bang/inflationary cosmology known as the "cyclic universe," in which space undergoes limitless epochs of reheating, expansion and cooling and in which the key events that smoothed and flattened the universe came before the last bang.
The cyclic universe is motivated, in part, by the recent discovery that the universe is entering an epoch of accelerated expansion.
Since the mid-1990s, my group has been playing a leading role establishing the experimental case for accelerated expansion and exploring the possibility that the acceleration is driven
by a dynamical energy component with negative pressure,
called ``quintessence."
A significant component of my group's current research is aimed at identifying the optimal observational tests
for distinguishing quintessence from a cosmological constant.
These studies lead inevitably to the question of why quintessence (or a cosmological constant) should dominate the universe today. In the standard big bang/inflationary picture, there is no natural explanation -- the additional energy density and its peculiar equation of state have to be put in by hand and they serve no apparent purpose. Therefore, we have been drawn to an alternative view of the history of the universe, motivated by string theory, in which quintessence turns out to play an essential role.
The cyclic model was inspired in part by string theory and M-theory which suggest that our
observable universe may lie in a three dimensional surface, a brane or
domain wall, embedded in a higher dimensional space with various possible
compactifications.
This intriguing concept first led us to introduce a proposal
for the early evolution of the universe, the
"ekpyrotic scenario"
based on the concept
that the hot big bang arose from a collision of branes in extra
dimensions. During the period in which the branes move towards one antoher, the universe becomes homogeneous, isotropic and flat, and nearly scale-invariant density perturbations are generated, all without any having any inflation. A few years later, it was realized that the interbrane potential energy can act as quintessence, and that the collisions can repeat over and over. Here the quintessence plays an essential role in causing the cycling to be a stable attractor-type behavior. Most recently, we have been exploring how cycling and branes can naturally explain why the quintessence energy is exponentially smaller than the Planck density. It appears that quintessence and the cyclic model fit together in a simple and compelling way.
The key test that will distinguish the big bang/inflationary picture from the cyclic picture is the detection (or non-detection) of the nearly scale-invariant spectrum of gravitational waves predicted by inflation, and perhaps also non-gaussianity. This has led our group to study the detection of gravitational waves by various methods (microwave background polarization, space-based detectors, pulsars, etc.) and how the combination can be used to test many quantitative aspects of cosmological models. Independently, we have been exploring how sensitive tests of general relativity at short and long distances can be used to test models of quintessence.
Numerical simulations of the gravitational clumping of dark matter in the early universe suggest that cold (non-relativistic) matter may gravitational collapse to form clumps that are too dense and too numerous compared to observations. We are exploring the possibility that these astrophysical observations indicate that the dark matter is strongly self-interacting, rather than weakly interacting, as conventionally assumed. Scattering of dark matter particles may cause the distribution of dark matter to be smoother in the galactic core and for there to be less clumped substructure within our galactic halo, in accordance with observations. Further studies of galactic and cluster substructure by gravitational lensing and other techniques could then be an important probe of dark matter interactions. We are exploring theoretical scenarios based on string theory and M-theory, and empirical methods for testing this possibility using highly sensitive space-borne bolometers.
In condensed matter physics, the focus has been on
quasicrystals,
novel solids with quasiperiodic atomic order which exhibit symmetries forbidden
to ordinary crystals (such as five-fold symmetry in two-dimensions and icosahedral
symmetry in three-dimensions).
We have proposed a new paradigm for the structure
of quaiscrystals, known as the "quasi-unit cell" picture, in which
atomic configuration can be decomposed into a single repeating cluster which
can overlap its neighbors by sharing atoms. The picture is being tested
by comparing predictions with the imaging and physical measurements of known
quasicrystals. If established, the quasi-unit cell picture offers a simple
way of characterizing the structure of quasicrystals and suggests simple
mechanisms to explain why they form and how they grow.
Independently, we are applying the geometric concepts to construct
photonic quasicrystals --
heterostructuresaimed at trapping, redirecting and guiding light.
 We have designed structures composed of two dielectric materials arranged in a quasiperiodic pattern, constructed macroscopic models based on these designed, , tested them using microwaves, and measured their scattering and light-trapping properties. The promising results have led us to work on improving he design and miniaturizing the structures for optical applications.
Paul
Steinhardt's Personal Homepage
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