arXiv subjects

Paul J. Steinhardt

Publications and source records attributed to Paul J. Steinhardt.

At least 37 records · Page 2Linked to original sources

arXiv2024

Ordered and disordered stealthy hyperuniform point patterns across spatial dimensions

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to real-space hard-spheres, whose densest configuration is conjectured to be disordered. We also extend the virial series previously suggested for disordered stealthy hyperuniform systems to higher dimensions in order to predict spatial decorrelation as function of dimension. This prediction is then borne out by numerical simulations of disordered stealthy hyperuniform ground states in dimensions $d=2$-$8$.

cond-mat.stat-mech↗

arXiv2024

Smoothing and flattening the universe through slow contraction versus inflation

In a systematic study, we use an equivalent pair of improved numerical relativity codes based on a tetrad-formulation of the classical Einstein-scalar field equations to examine whether slow contraction or inflation (or both) can resolve the homogeneity, isotropy and flatness problems. Our finding, based on a set of gauge/frame invariant diagnostics, is that slow contraction robustly and rapidly smooths and flattens spacetime beginning from initial conditions that are outside the perturbative regime of the flat Friedmann-Robertson-Walker metric, whereas inflation fails these tests. We present new numerical evidence supporting the conjecture that the combination of ultralocal evolution and an effective equation-of-state with pressure much greater than energy density is the key to having robust and rapid smoothing. The opposite of ultralocality occurs in expanding spacetimes, which is the leading obstruction to smoothing following a big bang.

gr-qc↗

arXiv2024

Stealthy and hyperuniform isotropic photonic bandgap structure in 3D

In photonic crystals the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic dielectric structures their photonic band structure is intrinsically anisotropic. However, for many applications, such as manufacturing artificial structural color materials or developing photonic computing devices, but also for the fundamental understanding of light-matter interactions, it is of major interest to seek materials with long range non-periodic dielectric structures which allow the formation of {\it isotropic} photonic band gaps. Here, we report the first ever 3D isotropic photonic band gap for an optimized disordered stealthy hyperuniform structure for microwaves. The transmission spectra are directly compared to a diamond pattern and an amorphous structure with similar node density. The band structure is measured experimentally for all three microwave structures, manufactured by 3D-Laser-printing for meta-materials with refractive index up to $n=2.1$. Results agree well with finite-difference-time-domain numerical investigations and a priori calculations of the band-gap for the hyperuniform structure: the diamond structure shows gaps but being anisotropic as expected, the stealthy hyperuniform pattern shows an isotropic gap of very similar magnitude, while the amorphous structure does not show a gap at all. The centimeter scaled microwave structures may serve as prototypes for micrometer scaled structures with bandgaps in the technologically very interesting region of infrared (IR).

physics.app-ph↗

arXiv2024

Stable Vacua with Realistic Phenomenology and Cosmology in Heterotic M-theory Satisfying Swampland Conjectures

We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in $E_8$. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the $B-L$ MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint -- as well as with $Λ$CDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.

hep-th↗

arXiv2023

Cosmological Bounces Induced by a Fermion Condensate

We show that it is possible for fermion condensation of the Nambu-Jona-Lasinio type to induce a non-singular bounce that smoothly connects a phase of slow contraction to a phase of expansion. A chiral condensate -- a non-zero vacuum expectation value of the spinor bilinear $\langle \barΨΨ\rangle$ -- can form spontaneously after a slow contraction phase smooths and flattens the universe and the Ricci-curvature exceeds a critical value. In this approach, a high density of spin-aligned free fermions is not required, which avoids the problem of generating a large anisotropy and initiating chaotic mixmaster behavior during the bounce phase.

gr-qc↗

arXiv2023

Initial conditions problem in cosmological inflation revisited

We present first results from a novel numerical relativity code based on a tetrad formulation of the Einstein-scalar field equations combined with recently introduced gauge/frame invariant diagnostics indicating that inflation does not solve the homogeneity and isotropy problem beginning from generic initial conditions following a big bang.

gr-qc↗

arXiv2023

Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties

Hyperuniform many-particle systems are characterized by a structure factor $S({\mathbf{k}})$ that is precisely zero as $|\mathbf{k}|\rightarrow0$; and stealthy hyperuniform systems have $S({\mathbf{k}})=0$ for the finite range $0 < |{\mathbf{k}}| \le K$, called the "exclusion region." Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing $S(\mathbf{k})$ in the exclusion region is computationally intensive as the system size becomes large. In this Letter, we present an improved methodology to generate such states using double-double precision calculations on GPUs that reduces the deviations from zero within the exclusion region by a factor of approximately $10^{30}$ for systems sizes more than an order of magnitude larger. We further show that this ultra-high accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small.

cond-mat.stat-mech↗

arXiv2022

Self-Similar One-Dimensional Quasilattices

We study 1D quasilattices, especially self-similar ones that can be used to generate two-, three- and higher-dimensional quasicrystalline tessellations that have matching rules and invertible self-similar substitution rules (also known as inflation rules) analogous to the rules for generating Penrose tilings. The lattice positions can be expressed in a closed-form expression we call {\it floor form}: $x_{n}=S(n-α)+(L-S)\lfloor κ(n-β)\rfloor$, where $L >S>0$ and $0<κ<1$ is an irrational number. We describe two equivalent geometric constructions of these quasilattices and show how they can be subdivided into various types of equivalence classes: (i) {\it lattice equivalent}, where any two quasilattices in the same lattice equivalence class may be derived from one another by a local decoration/gluing rule; (ii) {\it self-similar}, a proper subset of lattice equivalent where, in addition, the two quasilattices are locally isomorphic; and (iii) {\it self-same}, a proper subset of self-similar where, in addition, the two quasilattices are globally isomorphic (i.e.) identical up to rescaling). For all three types of equivalence class, we obtain the explicit transformation law between the floor form expression for two quasilattices in the same class. We tabulate (in Table I and Figure 5) the ten special self-similar 1D quasilattices relevant for constructing Ammann patterns and Penrose-like tilings in two dimensions and higher, and we explicitly construct and catalog the corresponding self-same quasilattices.

math-ph↗

arXiv2022

Coxeter Pairs, Ammann Patterns and Penrose-like Tilings

We identify a precise geometric relationship between: (i) certain natural pairs of irreducible reflection groups (``Coxeter pairs"); (ii) self-similar quasicrystalline patterns formed by superposing sets of 1D quasi-periodically-spaced lines, planes or hyper-planes (``Ammann patterns"); and (iii) the tilings dual to these patterns (``Penrose-like tilings"). We use this relationship to obtain all irreducible Ammann patterns and their dual Penrose-like tilings, along with their key properties in a simple, systematic and unified way, expanding the number of known examples from four to infinity. For each symmetry, we identify the minimal Ammann patterns (those composed of the fewest 1d quasiperiodic sets) and construct the associated Penrose-like tilings: 11 in 2D, 9 in 3D and one in 4D. These include the original Penrose tiling, the four other previously known Penrose-like tilings, and sixteen that are new. We also complete the enumeration of the quasicrystallographic space groups corresponding to the irreducible non-crystallographic reflection groups, by showing that there is a unique such space group in 4D (with nothing beyond 4D).

math-ph↗

arXiv2022

Entropy, Black holes, and the New Cyclic Universe

We track the evolution of entropy and black holes in a cyclic universe that undergoes repeated intervals of expansion followed by slow contraction and a smooth (non-singular) bounce. In this kind of cyclic scenario, there is no big crunch and no chaotic mixmaster behavior. We explain why the entropy following each bounce is naturally partitioned into near-maximal entropy in the matter-radiation sector and near-minimal in the gravitational sector, satisfying the Weyl curvature conditions conjectured to be essential for a cosmology consistent with observations. As a result, this kind of cyclic universe can undergo an unbounded number of cycles in the past and/or the future.

gr-qc↗

arXiv2022

Rapidly Descending Dark Energy and the End of Cosmic Expansion

If dark energy is a form of quintessence driven by a scalar field $ϕ$ evolving down a monotonically decreasing potential $V(ϕ)$ that passes sufficiently below zero, the universe is destined to undergo a series of smooth transitions. The currently observed accelerated expansion will cease; soon thereafter, expansion will come to end altogether; and the universe will pass into a phase of slow contraction. In this paper, we consider how short the remaining period of expansion can be given current observational constraints on dark energy. We also discuss how this scenario fits naturally with cyclic cosmologies and recent conjectures about quantum gravity.

astro-ph.CO↗

arXiv2021

Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields

We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear sigma model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann- Robertson-Walker (FRW) geometry for a wide range of inhomogeneous and anisotropic initial conditions. Ultimately, we find, the kinetic coupling causes the evolution to deflect away from flat FRW and towards a novel Kasner-like stationary point, but in general this occurs on time scales that are too long to be observationally relevant.

gr-qc↗

arXiv2021

Gap Sensitivity Reveals Universal Behaviors in Optimized Photonic Crystal and Disordered Networks

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast $α$ for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity $\mathcal{S}(α)\equiv dΔ(α)/dα$, the first derivative of the optimal gap-to-midgap ratio $Δ(α)$. In particular, for all our crystal networks, $\mathcal{S}(α)$ takes a universal form that is well approximated by the analytic formula for a one-dimensional quarter-wave stack, $\mathcal{S}_{\text{QWS}}(α)$. Even more surprisingly, the values of $\mathcal{S}(α)$ for our disordered networks converge to $\mathcal{S}_{\text{QWS}}(α)$ for sufficiently large $α$. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic heterostructures.

physics.optics↗

arXiv2021

The Effects of Multiple Modes and Reduced Symmetry on the Rapidity and Robustness of Slow Contraction

We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single fourier mode along only a single spatial direction are in general enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry. Particularly significant are shear effects that only become possible when variations are allowed along two or more spatial dimensions. Based on the numerical results, we conjecture that the counterintuitive enhancement occurs because more degrees of freedom are activated which drive spacetime away from an unstable Kasner fixed point and towards the stable Friedmann-Robertson-Walker fixed point.

gr-qc↗

arXiv2021

Ultralocality and Slow Contraction

We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, we find that the geometry first rapidly converges to an inhomogeneous, spatially-curved and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.

gr-qc↗

arXiv2020

Classically stable non-singular cosmological bounces

One of the fundamental questions of theoretical cosmology is whether the universe can undergo a non-singular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a non-singular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this letter, we examine cubic Galileon theories and present a procedure for explicitly constructing examples of a non-singular cosmological bounce without encountering any pathologies and maintaining a sub-luminal sound speed for co-moving curvature modes throughout the NEC violating phase. We also discuss the relation between our procedure and earlier work.

gr-qc↗

arXiv2020

Fully stable cosmological solutions with a non-singular classical bounce

We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order ${\cal L}_4$ Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.

gr-qc↗

arXiv2020

Robustness of slow contraction to cosmic initial conditions

We present numerical relativity simulations of cosmological scenarios in which the universe is smoothed and flattened by undergoing a phase of slow contraction and test their sensitivity to a wide range of initial conditions. Our numerical scheme enables the variation of all freely specifiable physical quantities that characterize the initial spatial hypersurface, such as the initial shear and spatial curvature contributions as well as the initial field and velocity distributions of the scalar that drives the cosmological evolution. In particular, we include initial conditions that are far outside the perturbative regime of the well-known attractor scaling solution. We complement our numerical results by analytically performing a complete dynamical systems analysis and show that the two approaches yield consistent results.

gr-qc↗