Perturbations in a regular bouncing Universe

TL;DR

This paper explores a toy model of a regular bouncing universe driven by an extra dimension, analyzing perturbations and their spectra, and finds challenges in matching realistic cosmological observations.

Contribution

It introduces a simple bouncing universe model with an extra time-like dimension and studies the evolution of perturbations, highlighting spectral issues.

Findings

Spectral index for scalar perturbations is -1.

Tensor perturbations have a deep blue spectrum.

Spectrum is sensitive to the bounce details.

Abstract

We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra time-like dimension, which leads to a sign flip of the $\rho^2$ term in the effective four dimensional Randall Sundrum-like description. We find a wide class of possible bounces: big bang avoiding ones for regular matter content, and big rip avoiding ones for phantom matter. Focusing on radiation as the matter content, we discuss the evolution of scalar, vector and tensor perturbations. We compute a spectral index of $n_s=-1$ for scalar perturbations and a deep blue index for tensor perturbations after invoking vacuum initial conditions, ruling out such a model as a realistic one. We also find that the spectrum (evaluated at Hubble crossing) is sensitive to the bounce. We conclude that it is challenging, but not impossible, for cyclic/ekpyrotic models to succeed, if one can find a regularized version.