Paul J. Steinhardt

Professor of Physics
Office Phone
214 Jadwin Hall


Albert Einstein Professor in Science. Professor of Physics
Director,  Princeton Center for Theoretical Science

My current research spans problems in cosmology, astrophysics, particle physics,  condensed matter physics planetary science and photonics. 

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.  Over the last decade, my research has turned to an alternative known as the "cyclic universe," in which the big bang is not the beginning of space and time but rather a bounce from a pre-existing phase of contraction into a phase of expansion accompanied by the creation of hot matter and radiation;  the key events that smoothed and flattened the universe occur before the last bang; dark energy plays a role in smoothing and flattening the universe prior to the next contraction phase and next big bang; and the entire cycle repeats every trillion years or so.  This is a very fruitful area of research.  We have recently found that there are numerous methods for smoothing and flattening the universe during a contracting phase (such as ekpyrotic and anamorphic mechanisms) and in having the universe bounce.  We are developing these ideas and seeking ways of distinguishing them observationally.  

Image removed.

The cyclic universe is motivated, in part, by the 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." More recently, the effort has turned to combine the idea of a slowly time-varying cosmological constant and a cyclic universe can naturally explain the small, positive value observed today.  Other topics  which our group continues to purse are alternative models of dark matter, such as strongly self-interacting elementary particles; modifications of Einstein gravity; time-variation of fundamental constants; and the implications of inflationary and cyclic cosmology for primordial gravitational waves and non-gaussian perturbations in the early universe.

Image removed.

In condensed matter physics, a long-term 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).  Quasicrystals are related to quasiperiodic tesselations, such as Penrose tilings.  Currently, we are exploring ways in which quasiperiodic tilings in three and four dimensions can be forced by local rules, which for quasicrystals represent finite-range interatomic interactions.  In the case of three dimensions, we will compare the forced tilings to the atomic configurations of real materials.

Image removed.

An intriguing question is whether quasicrystals can form naturally.   The issue is important for condensed matter physics because it provides insights into how easy and common it is for quasicrystals to form and because it may reveal new quasicrystallines solids not yet observed in the laboratory.  For geology, the discovery of natural quasicrystals would open new directions in mineralogy, raising questions about where and how these exotic solids form.  I organized a search which, after a decade, identified the first natural candidate in a mineral sample in a museum in Florence.  To prove the sample is natural has required numerous extraordinary steps, including:  a private eye-like investigation tracing the origin of the sample to a remote stream in Kamchatka in far eastern Russia; organizing a geological expedition in hopes of finding more samples; discovering new samples that show samples came from a meteorite that formed 4.5 billions years ago; conducting high pressure experiments at Argonne National Laboratory and using a gas gun at Caltech to collide raw materials so as to reproduce the conditions that may have formed the meteorite; the discovery of a second type of natural quasicrystal; and much more.


Image removed.

A possible application quasicrystals is photonics, heterostructures aimed 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.  Recently, we have extended this study to a new class of disordered structures, known as “hyperuniform disordered solids” or HUDS;  although the structures are isotropic and disordered, they exhibit surprising diffraction and band gap properties that make them optimal for some photonic applications.  The study suggests that hyperuniform structures may have interesting elastic, electronic and phononic properties, as well, and may be relevant to a variety of  biological and physical phenomena.

Selected Recent Publications



  • A. Ijjas and P. Steinhardt, “The anamorphic universe,” JCAP 1510,: 001 (2015).
  • L. Bindi, et al., "Natural quasicrystals with decagonal symmetry,” Science Reports 5, 9111  (2015).
  • A. Levy, A. Ijjas and P. Steinhardt,  “Scale-invariant perturbations in ekpyrotic cosmologies without fine-tunting of initial conditions,"Phys. Rev. D92: 063524 (2015).
  • J. Pollack, D. Spergel and P. Steinhardt, “Supermassive black holes from ultra-strongly self-interacting dark matter,”  Astrophys. J.  804, 131 (2015).
  • I. Bars, P. Steinhardt and N. Turok, " Dynamical String Tension in String Theory with Spacetime Weyl Invariance ,  Fortsh. der Physik 62, 901 (2014).
  • L.S. Hollister, et al., "Impact-induced shock and the formation of natural quasicrystals in the early solar system     ,   Nature Communications 5, 4040 (2014).
  • G. Nahal, et al., "Isotropic band gaps and freeform waveguides observed in hyperuniform disordered photonic solids,”   Frontiers in Optics  213, FW5E.3 (2013).



For further information, see