Essential Papers

We give here a list of papers by members of the group introducing the basic concepts underlying bouncing cosmologies.

A. Ijjas, P.J. Steinhardt
Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
Class.Quant.Grav. 33 (2016), p.044001. arXiv:1512.09010

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) p.023525. arXiv:1309.4480

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


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

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

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

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), 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. 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

the simplest known ekpyrotic theory that admits stable background solutions and generates a spectrum of nearly scale-invariant primordial perturbations with negligible non-gaussianity

J.-L. Lehners, P. McFadden, P.J. Steinhardt, N. Turok
Generating Ekpyrotic Curvature Perturbations Before the Big Bang
Phys.Rev. D76 (2007) p.103501. arXiv:0702153

a mechanism to generate curvature perturbations during the ekpyrotic phase using two fields – one that produces the ekpyrotic background and one that produces squeezed quantum fluctuations that are converted to curvature perturbations during the bounce phase


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

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


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

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. LINK

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. LINK

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


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