Two Field Matter Bounce Cosmology

TL;DR

This paper re-examines a non-singular Matter Bounce cosmology, analyzing how initial entropy fluctuations transfer into curvature fluctuations, resulting in nearly scale-invariant spectra with a blue tilt on small scales, and discusses their evolution through the bounce.

Contribution

It provides a detailed analysis of the transfer of entropy to curvature perturbations in a two-field Matter Bounce scenario, including their spectral properties and evolution through the bounce phase.

Findings

Curvature fluctuations become nearly scale-invariant on large scales.

Entropy fluctuations are initially scale-invariant but have smaller amplitude.

Both curvature and entropy fluctuations are blue-tilted on small scales after the bounce.

Abstract

We re-examine the non-singular Matter Bounce scenario first developed in [arXiv:1206.2382], which starts with a matter-dominated period of contraction and transitions into an Ekpyrotic phase of contraction. We consider both matter fields, the first of which plays the role of regular matter, and the second of which is responsible for the non-singular bounce. Since the dominant matter field is massive, the induced curvature fluctuations are initially not scale-invariant, whereas the fluctuations of the second scalar field (which are initially entropy fluctuations) are scale-invariant. We study the transfer of the initial entropy perturbations into curvature fluctuations in the matter-dominated phase of contraction and show that the latter become nearly scale invariant on large scales but are blue tilted on small scales. We study the evolution of both curvature and entropy fluctuations through the bounce, and show that both have a scale-invariant spectrum which is blue-tilted on small scales. However, we find that the entropy fluctuations have an amplitude that is much smaller than that of the curvature perturbations, due to gravitational amplification of curvature perturbations during the bounce phase.