Spectra of primordial fluctuations in two-perfect-fluid regular bounces

TL;DR

This paper analyzes scalar and tensor perturbations in two-fluid bouncing cosmological models, revealing that the Newtonian potential's growing mode does not match across the bounce and that tensor spectral index remains unaffected by negative energy fluids.

Contribution

It provides analytic solutions and detailed analysis of perturbations in two-fluid bounce models, clarifying mode evolution and spectral properties.

Findings

Growing mode of Newtonian potential does not match across the bounce.

Tensor spectral index is independent of negative energy fluid.

Analytic and numerical results are in agreement for specific cases.

Abstract

We introduce analytic solutions for a class of two components bouncing models, where the bounce is triggered by a negative energy density perfect fluid. The equation of state of the two components are constant in time, but otherwise unrelated. By numerically integrating regular equations for scalar cosmological perturbations, we find that the (would be) growing mode of the Newtonian potential before the bounce never matches with the the growing mode in the expanding stage. For the particular case of a negative energy density component with a stiff equation of state we give a detailed analytic study, which is in complete agreement with the numerical results. We also perform analytic and numerical calculations for long wavelength tensor perturbations, obtaining that, in most cases of interest, the tensor spectral index is independent of the negative energy fluid and given by the spectral index of the growing mode in the contracting stage. We compare our results with previous investigations in the literature.