A classical bounce: constraints and consequences

TL;DR

This paper investigates a simple cosmological bounce model driven by a massive scalar field, analyzing conditions for a successful bounce and inflation, and examining how perturbations evolve, with results compatible with observational data.

Contribution

It provides a phase space analysis of bounce conditions in a scalar field cosmology and studies the impact on scalar perturbations, highlighting the effects of initial conditions and spectral modifications.

Findings

Bounce requires fine-tuning of initial conditions.

Scalar perturbations are significantly modified during the bounce.

Resulting spectra can be compatible with WMAP data.

Abstract

We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general self-interacting potential and a background spacetime with positively curved spatial sections. By means of a phase space analysis, we give the conditions under which an initially contracting phase can be followed by a bounce and an inflationary phase lasting long enough (i.e., at least 60-70 e-folds) to suppress spatial curvature in today's observable universe. We find that, quite generically, this realization requires some amount of fine-tuning of the initial conditions. We study the effect of this background evolution on scalar perturbations by propagating an initial power-law power spectrum through the contracting phase, the bounce and the inflationary phase. We find that it is drastically modified, both spectrally (k-mode mixing) and in amplitude. It also acquires, at leading order, an oscillatory component, which, once evolved through the radiation and matter dominated eras, happens to be compatible with the WMAP data.