Bouncing Cosmology

A. Ijjas, P.J. Steinhardt

Bouncing Cosmology made simple
Class. Quantum Grav. 35 (2018) 135004

An intuitive way to illustrate how cosmological models with a classical (nonsingular) bounce generically resolve fundamental problems in cosmology. (Note that the earliest versions of bouncing cosmology (see Khoury et al. below) were based on colliding branes in extra dimensions; but those elements are inessential in current bouncing cosmology models, which are based on ordinary scalar fields in four space-time dimensions.)

A. Ijjas, P.J. Steinhardt

A new kind of cyclic universe
Phys.Lett. B795 (2019) 666-672

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.

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.

A. Ijjas, D. Garfinkle, P.J. Steinhardt, W.G. Cook

Smoothing and flattening the universe through slow contraction versus inflation
JCAP07(2024)077 (2024)

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.

D. Garfinkle, A. Ijjas, P.J. Steinhardt

Initial conditions problem in cosmological inflation revisited
arXiv:2404.00867 (2024)

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, F. Pretorius, P.J. Steinhardt, D. Garfinkle

Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields
JCAP 12 (2021) 030

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.

A. Ijjas, P.J. Steinhardt

Entropy, black holes and the new cyclic universe
Phys.Lett. B824 (2022) 136823

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 non-singular bounce. We show that the entropy problem of big bang cosmology is avoided and that the entropy following each bounce is naturally partitioned into near-maximal entropy in the matter-radiation sector and near-minimal in the gravitational sector, 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, A.P. Sullivan

The Effects of Multiple Modes and Reduced Symmetry on the Rapidity and Robustness of Slow Contraction
Phys. Lett. B820 (2021) 136490

We demonstrate that the rapidity and robustness of slow contraction are (contrary to intuition) significantly enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry. 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, W.G. Cook, F. Pretorius, P.J. Steinhardt, E.Y. Davies

Robustness of slow contraction to cosmic initial conditions
JCAP 08 (2020) 030

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.

A. Ijjas, A.P. Sullivan, F. Pretorius, P.J. Steinhardt and W.G. Cook

Ultralocality and Slow Contraction
JCAP 06 (2021) 013

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. The results show that, contrary to conventional lore, smoothing and flattening can occur over regions that are not causally connected due to the phenomenon of ultralocality that is characteristic in contracting universes.

W.G. Cook, I.A. Glushchenko, A. Ijjas, F. Pretorius, and P.J. Steinhardt

Supersmoothing through Slow Contraction
Phys.Lett. B808 (2020) 135690

This paper presents the compelling case that the most salient features of the universe — its homogeneity, isotropy and flatness on large scales — can only be explained by taking the `big bang’ out of the big bang theory (and inflation cosmology as well) and replacing with a period of slow contraction followed by a bounce. A fully non-perturbative analysis using the tools of numerical general relativity demonstrates 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, W.G. Cook, F. Pretorius, P.J. Steinhardt and E.Y. Davies

Robustness of Slow Contraction to Cosmic Initial Conditions
JCAP 08 (2020) 030

This paper and the paper above combine to make a compelling case that the most salient features of the universe — its homogeneity, isotropy and flatness on large scales — can only be explained by taking the `big bang’ out of the big bang theory and inflation as well) and replacing them with a period of slow contraction followed by a bounce.

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. B820 (2021) 136490

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

A. Ijjas, P.J. Steinhardt

Fully stable cosmological solutions with a nonsingular classical bounce
Phys.Lett. B764 (2017), pp.289–294.

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

A. Ijjas, P.J. Steinhardt

Classically stable nonsingular cosmological bounces 
Phys.Rev.Lett. 117 (2016) 121304.

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

A. Ijjas, F. Pretorius, P.J. Steinhardt

Stability and the Gauge Problem in Non-Perturbative Cosmology 
JCAP01 (2019) 015

The first steps towards fully non-perturbative cosmology: analyzing the linear mode stability in homogeneous and nearly homogeneous backgrounds and devising a valid scheme and diagnostics for numerical computation.

A. Ijjas, P.J. Steinhardt

Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
Class.Quant.Grav. 33 (2016) 044001

Brief overview of the current observational status of inflation and two different bouncing cosmologies

A. Ijjas, P.J. Steinhardt, A. Loeb

Scale-free primordial cosmology
Phys.Rev. D89 (2014) 023525

Introduction to the ekpyrotic smoothing mechanism based on a simple hydrodynamic treatment; reviews current observational status of ekpyrotic cosmology and compares to inflation

I. Bars, P.J. Steinhardt, N. Turok

Cyclic cosmology, conformal symmetry and the metastability of the Higgs 
Phys.Lett. B726 (2013), pp.50–55.

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), 1180-3.

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) 1436-9.

Original paper demonstrating how an ekpyrotic bouncing model can be made cyclic with each cycle entailing a period of expansion followed by a period of slow (ekpyrotic) contraction

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) 063514.

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

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), 123522.

“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.

B.-K. Xue, D. Garfinkle, F. Pretorius, P.J. Steinhardt

Nonperturbative analysis of the evolution of cosmological perturbations through a nonsingular bounce 
Phys.Rev. D88 (2013) 083509.

First ever application of numerical general relativity to study a nonsingular 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), 083537

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

George Carlin on the cyclic universe

Jim Carrey, Stephen Hawking and the Ekpyrotic Universe