A. Ijjas, P.J. Steinhardt, D. Garfinkle, W.G. Cook.
Smoothing and flattening the universe through slow contraction versus inflation | arXiv:2404.00867v2

Abstract. In a systematic study, we use an equivalent pair of improved numerical relativity codes 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.

D. Garfinkle, A. Ijjas, P.J. Steinhardt.
Initial conditions problem in cosmological inflation revisited | arXiv:2304.12150

Abstract. 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.

A. Ijjas.
Slow Contraction and the Weyl Curvature Hypothesis | arXiv:2304.10030

Abstract. Using the power of numerical relativity, we show that, beginning from generic initial conditions that are far from flat, homogeneous and isotropic and have a large Weyl curvature, a period of slow contraction rapidly drives spacetime towards vanishingly small Weyl curvature as the total energy density grows, thus providing a dynamical mechanism that satisfies the Weyl Curvature Hypothesis. We also demonstrate a tight correlation between the Weyl Curvature Hypothesis and ultralocal behavior for canonical scalar fields with a sufficiently steep negative potential energy density.

A. Ijjas.
Gauge/frame invariant variables for the numerical relativity study of cosmological spacetimes | arXiv:2304.07616

Abstract. To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly physical results cannot depend on the given formulation or gauge/frame choice. In this paper, we present a resolution of the gauge problem and, as an example, numerically implement it to evaluate our previous work on contracting spacetimes.

D. Shlivko.
Kinetically-driven ekpyrosis | arXiv:2207.10808

Abstract. We explore the possibility of a scalar field driving ekpyrotic contraction through a non-canonical kinetic energy density rather than a negative potential. We find that this kinetically-driven ekpyrosis ("k-ekpyrosis") can be achieved in a variety of models, including scalar field theories with power-law, polynomial, or DBI-like kinetic terms in the action. Of these examples, the ekpyrotic phase is best sustained in power-law models, which can generate large and constant equation-of-state parameters, followed by DBI-like models, which can exhibit dynamical attractors toward similarly large equations of state. We show that for a broad class of theories including these examples, phases of k-ekpyrosis are accompanied by preceding or concurrent phases of superluminality.

T. Kist, A. Ijjas.
The robustness of slow contraction and the shape of the scalar field potential | arXiv:2205.01519

Abstract. We use numerical relativity simulations to explore the conditions for a canonical scalar field φ minimally coupled to Einstein gravity to generate an extended phase of slow contraction that robustly smooths the universe for a wide range of initial conditions and then sets the conditions for a graceful exit stage. We show that to achieve robustness it suffices that the potential V(φ) is negative and M_Pl|V'/V|≥5 during the smoothing phase. We also show that, to exit slow contraction, the potential must have a minimum. Beyond the minimum, we find no constraint on the uphill slope including the possibility of ending on a positive potential plateau or a local minimum with V_min>0. Our study establishes ultralocality for a wide range of potentials as a key both to robust smoothing and to graceful exit.

C. Andrei, A. Ijjas, P.J. Steinhardt.
Rapidly Descending Dark Energy and the End of Cosmic Expansion | arXiv:2201.07704

Abstract. 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.

A. Ijjas
Numerical Relativity as a New Tool for Fundamental Cosmology | arXiv:2201.03752

Abstract. Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as a powerful new complementary tool for fundamental cosmology. To illustrate its power, we discuss applications of numerical relativity to studying the robustness of slow contraction and inflation in homogenizing, isotropizing and flattening the universe beginning from generic unsmooth initial conditions. In particular, we describe how recent numerical relativity studies of slow contraction have revealed a novel, non-linear smoothing mechanism based on ultralocality that challenges the conventional view on what is required to explain the large-scale homogeneity and isotropy of the observable universe.

A. Ijjas, F. Pretorius, P.J. Steinhardt and D. Garfinkle
Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields | arXiv:2109.09768

Abstract. 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.

A. Ijjas and P.J. Steinhardt
Entropy, Black holes, and the New Cyclic Universe | arXiv:2108.07101

Abstract. 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.

A. Ijjas, F. Pretorius, P.J. Steinhardt and A.P. Sullivan
The Effects of Multiple Modes and Reduced Symmetry on the Rapidity and Robustness of Slow Contraction | arXiv:2104.12293

Abstract. 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.

A. Ijjas, A.P. Sullivan, F. Pretorius, P.J. Steinhardt and W.G. Cook
Ultralocality and Slow Contraction | arXiv:2103.00584

Abstract. 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.

A. Ijjas and R. Kolevatov
Nearly scale-invariant curvature modes from entropy perturbations during graceful exit | arXiv:2102.03818

Abstract. In this Letter, we describe how a spectrum of entropic perturbations generated during a period of slow contraction can source a nearly scale-invariant spectrum of curvature perturbations on length scales larger than the Hubble radius during the transition from slow contraction to a classical non-singular bounce (the `graceful exit' phase). The sourcing occurs naturally through higher-order scalar field kinetic terms common to classical (non-singular) bounce mechanisms. We present a concrete example in which, by the end of the graceful exit phase, the initial entropic fluctuations have become negligible and the curvature fluctuations have a nearly scale-invariant spectrum with an amplitude consistent with observations.

A. Ijjas and R. Kolevatov
Sourcing curvature modes with entropy perturbations in non-singular bouncing cosmologies | arXiv:2012.08249

Abstract. The observed temperature fluctuations in the cosmic microwave background can be traced back to primordial curvature modes that are sourced by adiabatic and/or entropic matter perturbations. In this paper, we explore the entropic mechanism in the context of non-singular bouncing cosmologies. We show that curvature modes are naturally generated during `graceful exit,' i.e., when the smoothing slow contraction phase ends and the universe enters the bounce stage. Here, the key role is played by the kinetic energy components that come to dominate the energy density and drive the evolution towards the cosmological bounce.

A. Ijjas, W.G. Cook, F. Pretorius, P.J. Steinhardt and E.Y. Davies
Robustness of Slow Contraction to Cosmic Initial Conditions | arXiv:2006.04999

Abstract. 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.

W.G. Cook, I.A. Glushchenko, A. Ijjas, F. Pretorius, and P.J. Steinhardt
Supersmoothing through Slow Contraction | arXiv:2006.01172

Abstract. Performing a fully non-perturbative analysis using the tools of numerical general relativity, we demonstrate that a period of 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.

G. Montefalcone, P.J. Steinhardt and D. Wesley
Dark Energy, Extra Dimensions, and the Swampland | arXiv:2005.01143

Abstract. Perhaps the greatest challenge for fundamental theories based on compactification from extra dimensions is accommodating a period of accelerated cosmological expansion. Previous studies have identified constraints imposed by the existence of dark energy for two overlapping classes of compactified theories: (1) those in which the higher dimensional picture satisfies certain metric properties selected to reproduce known low energy phenomenology; or (2) those derived from string theory assuming they satisfy the Swampland conjectures. For either class, the analyses showed that dark energy is only possible if it takes the form of quintessence. In this paper, we explore the consequences for theories that belong to both classes and show that the joint constraints are highly restrictive, leaving few options.

A. Ijjas and P.J. Steinhardt
A New Kind of Cyclic Universe | arXiv:1904.08022

Abstract. Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically, but the scale factor grows by an exponential factor from one cycle to the next. The resulting cosmology not only resolves the homogeneity, isotropy, flatness and monopole problems and generates a nearly scale invariant spectrum of density perturbations, but it also addresses a number of age-old cosmological issues that big bang inflationary cosmology does not. There may also be wider-ranging implications for fundamental physics, black holes and quantum measurement.

A. Ijjas, F. Pretorius, P.J. Steinhardt
Stability and the Gauge Problem in Non-Perturbative Cosmology | arXiv:1809.07010

Abstract. In this paper, we describe the first steps towards fully non-perturbative cosmology. We explain why the conventional methods used by cosmologists based on the ADM formulation are generally inadequate for this purpose and why it is advantageous instead to adapt the harmonic formulation pioneered and utilized in mathematical and numerical relativity. Here we focus on using this approach to evaluating the linear mode stability in homogeneous and nearly homogeneous backgrounds and devising a valid scheme and diagnostics for numerical computation. We also briefly touch on the relevance of these methods for extracting cosmological observables from non-perturbative simulations.

P. Ade et al. (including A.Ijjas)
The Simons Observatory: Science goals and forecasts | arXiv:1808.07445

Abstract. The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. [...] Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The SATs will target the largest angular scales observable from Chile, mapping ~10% of the sky to a white noise level of 2 μK-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, r, at a target level of σ(r)=0.003. The LAT will map ~40% of the sky at arcminute angular resolution to an expected white noise level of 6 μK-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the LSST sky region and partially with DESI. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources.

P. Agrawal, G. Obied, P.J. Steinhardt, C. Vafa
On the Cosmological Implications of the String Swampland | arXiv:1806.09718

Abstract. We study constraints imposed by two proposed string Swampland criteria on cosmology. These criteria involve an upper bound on the range traversed by scalar fields as well as a lower bound on |∇_ϕV|/V when V > 0. We find that inflationary models are generically in tension with these two criteria. Applying these same criteria to dark energy in the present epoch, we find that specific quintessence models can satisfy these bounds and, at the same time, satisfy current observational constraints. Assuming the two Swampland criteria are valid, we argue that the universe will undergo a phase transition within a few Hubble times. These criteria sharpen the motivation for future measurements of the tensor-to-scalar ratio r and the dark energy equation of state w, and for tests of the equivalence principle for dark matter.

A. Ijjas, P.J. Steinhardt
Bouncing Cosmology made simple | arXiv:1803.01961

Abstract. We introduce the "wedge diagram," an intuitive way to illustrate how cosmological models with a classical (non-singular) bounce generically resolve fundamental problems in cosmology. These include the well-known horizon, flatness, and inhomogeneity problems; the small tensor-to-scalar ratio observed in the cosmic microwave background; the low entropy at the beginning of a hot, expanding phase; and the avoidance of quantum runaway. The same diagrammatic approach can be used to compare with other cosmological scenarios.