All Papers – Bouncing Cosmology

INTRODUCTORY PAPERS

A. Ijjas and P.J. Steinhardt
Bouncing Cosmology made simple
Class.Quant.Grav. 35 (2018), p.135004, arXiv:1803.01961

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.

A. Ijjas and P.J. Steinhardt
A New Kind of Cyclic Universe
Phys.Lett.B 795 (2019), p.666, arXiv:1904.08022

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.

A. Ijjas and P.J. Steinhardt
Entropy, Black holes, and the Universe
Phys.Lett.B 824 (2022), p.136823, arXiv:2108.07101

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.

M. Khaldieh, A.I. Rosenzweig and P.J. Steinhardt
Causal horizons, geodesic completeness and stability in slow contraction cosmology
Phys. Lett. B 880 (2026) 140851, arXiv:2607.07815

We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, slow contraction admits a stable past attractor asymptoting to Minkowski space, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy).

A. Levy, A. Ijjas, P.J. Steinhardt
Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning of initial conditions
Phys.Rev. D92 (2015), p.063524. arXiv:1506.01011

A simple ekpyrotic theory that admits stable background solutions and generates a spectrum of nearly scale-invariant primordial perturbations with negligible non-gaussianity.

N. Itzhaki, U. Peleg and P.J. Steinhardt
Instant Folded Strings, Dark Energy and a Cyclic Bouncing Universe
JCAP05(2026)084, arXiv:2508.09745.

We present a wholly self-consistent, complete cyclic bouncing cosmology based on components drawn from string theory and constructed in a way that is under perturbative control throughout. The cyclic evolution is governed by standard dilaton-gravity and a second field that becomes massless at an enhanced symmetry point (ESP) that prevents the dilaton from running all the way to zero coupling. A central role is played by instant folded strings (IFSs) – fundamental strings with the unusual property of extending far beyond the string length and violating the Null Energy Condition (NEC). They enable cosmological bounces and initiate transient epochs of dark-energy domination.

J. Khoury, B.A. Ovrut, P.J. Steinhardt, N. Turok
The ekpyrotic universe: Colliding branes and the origin of the hot big bang
Phys.Rev. D64 (2001), p. 123522. arXiv:0103239

The historical paper, introducing the idea of smoothing and flattening the universe through ekpyrotic contraction
Note: the colliding brane picture and the use of extra dimensions presented here were inspirations for the ekpyrotic concept but are not required or used in most current models; the simplest models today are based on ordinary scalar fields in three spatial dimensions, as illustrated by most of the examples on this page.

A. Ijjas, W.G. Cook, F. Pretorius, P.J. Steinhardt and E.Y. Davies
Robustness of Slow Contraction to Cosmic Initial Conditions
JCAP08(2020)030, arXiv:2006.04999

We describe in detail how to construct numerical relativity simulations of cosmological scenarios which show that the universe is smoothed and flattened by undergoing a phase of slow contraction. 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 slow contraction. We complement our numerical results by analytically performing a complete dynamical systems analysis and show that the numerical and analytic approaches yield consistent results.

A. Ijjas, P.J. Steinhardt, D. Garfinkle and W.G. Cook
Smoothing and flattening the universe through slow contraction versus inflation
JCAP07(2024)077, arXiv:2404.00867

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. We show 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 numerical evidence that the combination of ultralocal evolution and slow contraction 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.

J. Shterenberg, D. Garfinkle, A. I. Rosenzweig, D. Shlivko and P.J. Steinhardt.
Anti-ultralocality and plateau models of inflation | arXiv:2608.24997

NUMERICAL GENERAL RELATIVITY & COSMOLOGY

J. Shterenberg, D. Garfinkle, A. I. Rosenzweig, D. Shlivko and P.J. Steinhardt.
Anti-ultralocality and plateau models of inflation | arXiv:2608.24997

Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein–scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations either prevents inflation from lasting for enough e-folds or triggers a phase of quantum runaway and an unpredictive multiverse.

A. Ijjas, P.J. Steinhardt, D. Garfinkle and W.G. Cook
Smoothing and flattening the universe through slow contraction versus inflation
JCAP07(2024)077, arXiv:2404.00867

D. Garfinkle, A. Ijjas, and P.J. Steinhardt
Initial conditions problem in cosmological inflation revisited
Phys.Lett.B 843 (2023), p.138028, arXiv:2304.12150

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
Numerical Relativity as a New Tool for Fundamental Cosmology
Physics 4 (2022), p.301, arXiv:2201.03752

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.

A. Ijjas, F. Pretorius, P.J. Steinhardt and D. Garfinkle
Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields
JCAP12(2021)030, arXiv:2109.09768

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.

A. Ijjas, A.P. Sullivan, F. Pretorius, P.J. Steinhardt and W.G. Cook
Ultralocality and Slow Contraction
JCAP06(2021)013, arXiv:2103.00584

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.

A. Ijjas, W.G. Cook, F. Pretorius, P.J. Steinhardt and E.Y. Davies
Robustness of Slow Contraction to Cosmic Initial Conditions
JCAP08(2020)030, arXiv:2006.04999

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.

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
Phys.Lett.B 820 (2021), p.136490, arXiv:2104.12293

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 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..

W.G. Cook, I.A. Glushchenko, A. Ijjas, F. Pretorius, and P.J. Steinhardt
Supersmoothing through Slow Contraction
Phys.Lett.B 808 (2020), p.135690, arXiv:2006.01172

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.

A. Ijjas, F. Pretorius and P.J. Steinhardt
Stability and the Gauge Problem in Non-Perturbative Cosmology
JCAP01(2019)015, arXiv:1809.07010

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 evaluate the linear mode stability in homogeneous and nearly homogeneous backgrounds and devising a valid scheme and diagnostics for numerical computation.

B. Xue, D. Garfinkle, F. Pretorius, P.J. Steinhardt
Nonperturbative analysis of the evolution of cosmological perturbations through a nonsingular bounce
Phys.Rev. D88 (2013), p.083509. arXiv:1308.3044

First application of numerical general relativity to study a non-singular cosmological bounce; using a simple toy model, smooth evolution of perturbations through the bounce is demonstrated

D. Garfinkle, W.-C. Lim, F. Pretorius, P.J. Steinhardt
Evolution to a smooth universe in an ekpyrotic contracting phase with w > 1
Phys.Rev. D78 (2008), p.083537, arXiv:0808.0542

First application of numerical general relativity to cosmology showing that ekpyrotic contraction is a powerful smoother and flattener, highly insensitive to initial conditions.

SMOOTHING CONTRACTION MECHANISMS

J. Erickson, D. Wesley, P.J. Steinhardt, N. Turok
Kasner and Mixmaster behavior in universes with equation of state w > 1
Phys.Rev. D69 (2004) p.063514. arXiv:0312009

How the ekpyrotic mechanism makes it possible to suppress chaotic mixmaster (BKL) behavior during the contracting phase and preserve homogeneity.

T. Kist, and A. Ijjas
The robustness of slow contraction and the shape of the scalar field potential
JCAP08(2022)046, arXiv:2205.01519.

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. 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.

D. Shlivko
Kinetically-driven ekpyrosis
Phys.Rev.D 106 (2022), p.043508, arXiv:2207.10808.

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. 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.

A. Ijjas, P.J. Steinhardt
The anamorphic universe
JCAP 10 (2015), p.1. arXiv:1507.03875

A novel bouncing cosmology with a non-ekpyrotic mechanism for smoothing and flattening the universe.

J. Khoury, B.A. Ovrut, P.J. Steinhardt, N. Turok
The ekpyrotic universe: Colliding branes and the origin of the hot big bang
Phys.Rev. D64 (2001), p. 123522. arXiv:0103239

“The” historical paper, introducing the idea of smoothing and flattening the universe through ekpyrotic contraction
Note: the colliding brane picture and the use of extra dimensions presented here were inspirations for the ekpyrotic concept but are not required or used in most current models; the simplest models today are based on ordinary scalar fields in three spatial dimensions, as illustrated by most of the examples on this page.

COSMOLOGICAL BOUNCE MECHANISMS

A. Ijjas
Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutions
JCAP02(2018)007, arXiv:1710.05990

In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions with classically stable behavior for all modes with wavelengths above the Planck scale where: (a) the solution involves a stage of null-energy condition violation during which gravity is described by a modification of Einstein’s general relativity; and (b) the solution reduces to Einstein gravity both before and after the null-energy condition violating stage. Similar considerations apply to galilean genesis scenarios.

A. Ijjas, P.J. Steinhardt
Fully stable cosmological solutions with a non-singular classical bounce
Phys.Lett. B764 (2017), pp.289–294, arXiv:1609.01253

The first example of a non-pathological, geodesically complete cosmology with a non-singular bounce in which the pre-bounce evolution is described by Horndeski gravity.

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A. Ijjas, P.J. Steinhardt
Classically stable nonsingular cosmological bounces
Phys.Rev.Lett. 117 (2016), p.121304. arXiv:1606.08880

The first proof that violation of the null energy condition and a non-singular bounce stage can be achieved in Horndeski theories without generating any pathologies.

BOUNCING & CYCLIC COSMOLOGY

A. Ijjas and P.J. Steinhardt
A New Kind of Cyclic Universe
Phys.Lett.B 795 (2019), p.666, arXiv:1904.08022.

A. Ijjas and P.J. Steinhardt
Entropy, Black holes, and the Universe
Phys.Lett.B 824 (2022), p.136823, arXiv:2108.07101.

I. Bars, P.J. Steinhardt, N. Turok
Cyclic cosmology, conformal symmetry and the metastability of the Higgs
Phys.Lett. B726 (2013), pp.50–55, arxiv.org/abs/1307.8106

Example using the metastable Higgs field in the Standard Model for obtaining geodesically-complete, classical, cyclic cosmological solutions.

P.J. Steinhardt, N. Turok
Why the Cosmological Constant is Small and Positive
Science 312 (2006), p.1180, arxiv:0605173

Proposal to explain why the cosmological constant is naturally small if the universe is cyclic.

P.J. Steinhardt, N. Turok
A Cyclic Model of the Universe
Science 296 (2002), p.1436. arxiv: 0111030

Original paper demonstrating how an ekpyrotic bouncing model based on regularly colliding branes in a can be made cyclic with each cycle entailing a period of expansion followed by a period of slow (ekpyrotic) contraction.

PERTURBATIONS

A. Ijjas and R. Kolevatov
Nearly scale-invariant curvature modes from entropy perturbations during graceful exit
Phys.Rev.D 103 (2021), p.L101302, arXiv:2102.03818

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 consistent with observations.

A. Ijjas and R. Kolevatov
Sourcing curvature modes with entropy perturbations in non-singular bouncing cosmologies
JCAP06(2021)012, arXiv:2012.08249

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. Levy, A. Ijjas, P.J. Steinhardt
Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning of initial conditions
Phys.Rev. D92 (2015), p.063524, arXiv:1506.01011

A simple ekpyrotic theory that admits stable background solutions and generates a spectrum of nearly scale-invariant primordial perturbations with negligible non-gaussianity.

DARK ENERGY & DARK MATTER

N. Patino and P.J. Steinhardt
Particle production by time-varying dark energy and the end of cosmic expansion
JCAP05(2026)050, arXiv:2512.15860

We consider various possible consequences of time-varying dark energy due to a quintessence scalar field whose energy density is partially converted to particles as the field evolves down its potential. This particle production acts as a source of thermal friction on the field that can make it difficult to distinguish whether dark energy is due to a radiating field rolling down a steep potential, a purely self-interacting field moving down a flatter potential, or a cosmological constant. We take special interest in the case where a steep potential rapidly changes from positive to negative as the field evolves, resulting in the end of cosmic expansion and the beginning of slow contraction.

D. Shlivko and P.J. Steinhardt
Assessing observational constraints on dark energy
Phys.Lett.B 855 (2024), p.138826, arXiv:2405.03933

Observational constraints on time-varying dark energy (e.g., quintessence) are commonly presented on a `w_0-w_a plot’ that assumes the equation of state of dark energy strictly satisfies w(z) = w0 + wa z/(1 + z) as a function of the redshift z. Recent observations favor a sector of the w0-wa plane suggesting that the equation of state underwent a transition from violating the null energy condition (NEC) at large z to obeying it at small z. In this paper, we demonstrate that this impression is misleading by showing that simple quintessence models satisfying the NEC for all z predict an observational preference for the same sector.

D. Shlivko, P.J. Steinhardt and C.L. Steinhardt
Optimal parameterizations for observational constraints on thawing dark energy
JCAP06(2025)054, arXiv:2504.02028

Time-varying dark energy is often modeled in observational analyses through generic parameterizations of its equation of state w(z), which typically use two free parameters (w_0 and w_a) to span a broad range of behaviors as a function of redshift. However, this broad range of behaviors can only approximately capture the dynamics of any given microphysical theory of dark energy. A complementary approach is to use targeted parameterizations designed to model specific classes of dynamical dark energy with greater precision. We find that a targeted parameterization derived from a Padé expansion of w(z) is the most reliable of these.

C. Andrei, A. Ijjas andP.J. Steinhardt
Rapidly Descending Dark Energy and the End of Cosmic Expansion
PNAS 119 (2022), e2200539119, arXiv:2201.07704

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.

STRINGS & COSMOLOGY

A. Bedroya and P.J. Steinhardt.
Holographic constraints on the string landscape | arXiv:2511.15784

We show that holography imposes strong and general constraints on scalar field potentials in the string landscape, ruling out potentials with extended plateaus, excessively steep or shallow asymptotics, certain zero crossings, and specific alignments of stable AdS minima in moduli space. Taken together, these constraints exclude the leading proposals to realize scale-separated AdS vacua and metastable de Sitter vacua in the string theory landscape such as DGKT and KKLT.

A.Bedroya and P.J. Steinhardt.
Holography vs. scale separation | arXiv:2509.25313

In this work, we point out a contradiction between holography and scale-separated AdS (i.e. parametrically large mass gap) in string theory. Namely, there must exist a scalar field trajectory that follows the gradient of the scalar potential to the asymptotic region of the scalar field space in which limit V∼m^α, where α≤2 is a constant and m is the mass scale of the lightest tower of states. Barring fine-tuning, our conclusions apply to other Ricci-flat flux compactifications including the KKLT scenario which relies on scale separation to obtain a metastable de Sitter uplift.

N. Itzhaki, U. Peleg and P.J. Steinhardt
Instant Folded Strings, Dark Energy and a Cyclic Bouncing Universe
JCAP05(2026)084, arXiv:2508.09745

A. Bedroya, H. Lee and P.J. Steinhardt.
A species scale-driven breakdown of effective field theory in time-dependent string backgrounds | arXiv:2504.13260

We present a novel way in which effective field theory (EFT) can break down in cosmological string backgrounds depending on the behavior of the quantum gravity cutoff in infinite distance limits, known as the species scale. Namely, EFT can break down if the species scale falls off so rapidly as the Friedmann-Robertson-Walker (FRW) scale factor grows from some initial value to some final value such that the physical momentum of an initial Hubble-sized perturbation grows to exceed the species scale. Our bound is proportional to the Trans-Planckian Censorship Conjecture (TCC) bound, with the advantage that it applies to any FRW solution in the string landscape.

A. Bedroya, Q. Lu and P.J. Steinhardt
TCC in the interior of moduli space and its implications for the string landscape and cosmology
JHEP08(2025)007, arXiv:2407.08793

The case for the Transplanckian Censorship Conjecture (TCC) is strengthened, implying a new set of complex and highly nonlinear constraints across the entire string landscape which may make inflation impossible and restricts the ways dark energy can be incorporated in quantum gravity.

C. Deffayet, B.A. Ovrut and P.J. Steinhardt
Stable Vacua with Realistic Phenomenology and Cosmology in Heterotic M-theory Satisfying Swampland Conjectures
JHEP07(2024)288, arXiv:2401.04828

We elucidate, in detail, the mathematical and computational methods required to utilize the protocol described in the paper listed below. 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. 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 ΛCDM cosmology.

C. Deffayet, B.A. Ovrut and P.J. Steinhardt
Moduli axions, stabilizing moduli and the large field Swampland conjecture in Heterotic M-theory
Phys.Rev.D 109 (2024), p.126004, arXiv:2312.04656

We compute the potential energy for the dilaton, complex structure and Kahler moduli and search of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds. We derive a potential that combines the non-perturbative complex structure, gaugino condensate and worldsheet instanton superpotentials in theories in which the hidden sector contains an anomalous U(1) structure group. We obtain explicit examples in which potential has a global minimum zero vacuum density or a metastable minimum with positive vacuum density.

OBSERVATIONS

P. Ade et al. (including A.Ijjas)
The Simons Observatory: Science goals and forecasts
JCAP02(2019)056, arXiv:1808.07445

The Simons Observatory (SO) is a cosmic microwave background experiment being built on Cerro Toco in Chile, that has already begun making observations. This is a planning document that describes the scientific goals of the experiment, motivate the design, and forecast its performance. This includes characterizing the primordial perturbations, measuring the number of relativistic species and the mass of neutrinos, testing for deviations from a cosmological constant, improving our understanding of galaxy evolution, and constraining the duration of reionization.