Scalar perturbations in an $\alpha'$-regularised cosmological bounce

TL;DR

This paper studies scalar perturbations in non-singular bouncing cosmologies with string theory corrections, revealing that previous singular equations are inadequate and providing new equations and numerical results showing a blue spectrum after the bounce.

Contribution

It introduces a new system of first-order equations for scalar perturbations in regularized bouncing universes, improving upon previous singular evolution equations.

Findings

Scalar perturbations cannot be described by homogeneous second-order equations in regularized models.

Numerical simulations show a blue spectral distribution of perturbations after the bounce.

Both metric and dilaton fluctuations produce a blue spectrum long after the transition.

Abstract

We consider the evolution of scalar perturbations in a class of non-singular bouncing universes obtained with higher-order corrections to the low-energy bosonic string action. We show that previous studies have relied on a singular evolution equation for the perturbations. From a simple criterium we show that scalar perturbations cannot be described at all times by an homogeneous second-order perturbation equation in pre-big bang type universes if we are to regularise the background evolution with higher-order curvature and string coupling corrections, and we propose a new system of first-order coupled differential equations. Given a bouncing cosmological background with inflation driven by the kinetic energy of the dilaton field, we obtain numerically the final power spectra generated from the vacuum quantum fluctuations of the metric and the dilaton field during inflation. Our result shows that both Bardeen's potential, $\Phi(\eta,k)$, and the curvature perturbation in the uniform curvature gauge, ${\mathcal R}(\eta,k)$, lead to a blue spectral distribution long after the transition.