Evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: Indications for a no-go theorem in single field matter bounce cosmologies

TL;DR

This paper investigates the evolution of cosmological perturbations through a nonsingular bounce in single scalar field models, revealing a fundamental tension between achieving low tensor-to-scalar ratios and acceptable non-Gaussianity levels, suggesting a no-go theorem.

Contribution

It demonstrates that in single scalar field matter bounce cosmologies, growth of curvature perturbations and non-Gaussianities during the bounce are incompatible with observational constraints, indicating a fundamental limitation of such models.

Findings

Limited growth of curvature perturbations due to conservation on super-Hubble scales.

Enhanced non-Gaussianity parameter $f_{NL}$ during the bounce if perturbations grow.

A tension exists between low tensor-to-scalar ratio and acceptable non-Gaussianity levels.

Abstract

Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the nontrivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter $f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem that rules out any single field matter bounce cosmology starting with vacuum initial conditions for the fluctuations.