A Briefing on the Ekpyrotic/Cyclic Universe

TL;DR

The paper surveys the ekpyrotic/cyclic model as an inflation alternative, outlining a four-dimensional effective action with a scalar $\phi$ encoding brane separation and a multi-region potential $V(\phi)$ that drives slow contraction and a brane-collision bounce. It demonstrates a cosmological no-hair attractor for slow contraction with $w>1$ and shows that a nearly scale-invariant spectrum can arise in either slow-roll inflation ($\bar{\epsilon}\ll 1$) or slow contraction ($\bar{\epsilon}\gg 1$), related by the duality $\bar{\epsilon}\to 1/\bar{\epsilon}$. The spectrum is described by $n_s-1 \approx -\frac{2}{(1-\bar{\epsilon})^2}\left\{ \bar{\epsilon} - \frac{(1-\bar{\epsilon}^2)}{2}\frac{d\ln\bar{\epsilon}}{d{\cal N}}\right\}$, with inflation and ekpyrotic limits given by $(n_s-1)_{inf} \approx -2\bar{\epsilon} + \frac{d\ln\bar{\epsilon}}{d{\cal N}}$ and $(n_s-1)_{ek} \approx -\frac{2}{\bar{\epsilon}} - \frac{d\ln\bar{\epsilon}}{d{\cal N}}$. The authors discuss the need for a viable bounce (as proposed by Seiberg–Tolley) and the observational signature of gravitational waves, concluding that even if a bounce is not realized, the ekpyrotic program broadens cosmology and informs inflationary theory.

Abstract

This is a short overview of the ekpyrotic/cyclic model of the universe, an alternative to the standard big bang inflationary paradigm.

Figures (1)

• Figure 1.: Various allowed forms of cyclic potentials.