Nonperturbative analysis of the evolution of cosmological perturbations through a nonsingular bounce

TL;DR

This paper investigates the evolution of cosmological perturbations through a nonsingular bounce using nonperturbative methods, demonstrating that small, observationally consistent perturbations can pass through the bounce with preserved scale invariance.

Contribution

It introduces a nonperturbative approach, including numerical simulations and covariant formalism, to analyze the behavior of perturbations during a nonsingular cosmological bounce.

Findings

Small perturbations pass through the bounce with negligible nonlinearity effects.

Scale invariance of perturbations is preserved across the bounce.

Regions with significant inhomogeneity disrupt the bounce.

Abstract

In bouncing cosmology, the primordial fluctuations are generated in a cosmic contraction phase before the bounce into the current expansion phase. For a nonsingular bounce, curvature and anisotropy grow rapidly during the bouncing phase, raising questions about the reliability of perturbative analysis. In this paper, we study the evolution of adiabatic perturbations in a nonsingular bounce by nonperturbative methods including numerical simulations of the nonsingular bounce and the covariant formalism for calculating nonlinear perturbations. We show that the bounce is disrupted in regions of the universe with significant inhomogeneity and anisotropy over the background energy density, but is achieved in regions that are relatively homogeneous and isotropic. Sufficiently small perturbations, consistent with observational constraints, can pass through the nonsingular bounce with negligible alteration from nonlinearity. We follow scale invariant perturbations generated in a matter-like contraction phase through the bounce. Their amplitude in the expansion phase is determined by the growing mode in the contraction phase, and the scale invariance is well preserved across the bounce.