Ekpyrotic and Cyclic Cosmology

TL;DR

Ekpyrotic and cyclic cosmology present a brane-based picture where the big bang is a collision between boundary branes in a 5D bulk. A slow, ultra-stiff contraction (the ekpyrotic phase) flattens and homogenizes the universe, suppressing chaotic behavior and resolving the standard cosmological puzzles, while generating cosmological perturbations through multi-field entropy modes that can become nearly scale-invariant after conversion to curvature perturbations. The cyclic model weaves ekpyrosis with a dark-energy–driven expansion and a non-singular (or near) bounce, enabling endless cosmic cycles; its viability hinges on the perturbation spectrum, non-Gaussianity, and a consistent 4D EFT embedding in heterotic M-theory. Distinct observational signatures—most notably a blue tensor spectrum and sizeable non-Gaussianity depending on the conversion mechanism—offer clear tests to distinguish this framework from inflation.

Abstract

Ekpyrotic and cyclic cosmologies provide theories of the very early and of the very late universe. In these models, the big bang is described as a collision of branes - and thus the big bang is not the beginning of time. Before the big bang, there is an ekpyrotic phase with equation of state w=P/rho >> 1 (where P is the average pressure and rho the average energy density) during which the universe slowly contracts. This phase resolves the standard cosmological puzzles and generates a nearly scale-invariant spectrum of cosmological perturbations containing a significant non-gaussian component. At the same time it produces small-amplitude gravitational waves with a blue spectrum. The dark energy dominating the present-day cosmological evolution is reinterpreted as a small attractive force between our brane and a parallel one. This force eventually induces a new ekpyrotic phase and a new brane collision, leading to the idea of a cyclic universe. This review discusses the detailed properties of these models, their embedding in M-theory and their viability, with an emphasis on open issues and observational signatures.

Figures (12)

• Figure 1: The braneworld picture of our universe. Think of a sandwich: the filling is the 5-dimensinonal bulk spacetime, which is bounded by the two pieces of bread a.k.a. the 4-dimensional boundary branes. There is no space "outside" of the sandwich, but the branes can be infinite in all directions perpendicular to the line segment. In the M-theory embedding, there are 6 additional internal dimensions at each 5-dimensional spacetime point.
• Figure 2: The potential during ekpyrosis is negative and steeply falling; it can be modeled by the exponential form $V(\phi)=-V_0 e^{-c\phi}.$
• Figure 3: A line segment represented as the orbifold $S^1/\mathbb{Z}_2.$ The thick dots represent the orbifold fixed points.
• Figure 4: The compactified Milne mod $\mathbb{Z}_2$ space describes the collision of two boundary branes, embedded in Minkowski space.
• Figure 5: This figure shows the evolution of the kinetic function $P(X)$ and of the potential $V(\phi)$ during the phases of ekpyrosis and bounce. Note that the field starts at approximately zero potential energy and moving very slowly, so that $\rho \sim -\dot{\pi} +V \approx 0.$ Then, during the ekpyrotic phase, the potential is negative, implying that $\dot{\pi}<0$ and hence $\dot{H}<0.$ Subsequently, during the ghost condensate phase, the potential shoots back up to positive values, implying that $\dot{\pi}>0$ and thus $\dot{H}>0,$i.e. the universe starts reverting from contraction to expansion. Figure reproduced with permission from Buchbinder:2007ad.