Primordial perturbations in a nonsingular bouncing universe model

Abstract

We construct a simple non singular cosmological model in which the currently observed expansion phase was preceded by a contraction. This is achieved, in the framework of pure general relativity, by means of a radiation fluid and a free scalar field having negative energy. We calculate the power spectrum of the scalar perturbations that are produced in such a bouncing model and find that, under the assumption of initial vacuum state for the quantum field associated with the hydrodynamical perturbation, this leads to a spectral index n S = −1. The matching conditions applying to this bouncing model are derived and shown to be different from those in the case of a sharp transition. We find that if our bounce transition can be smoothly connected to a slowly contracting phase, then the resulting power spectrum will be scale invariant.

Propagation of adiabatic and entropy perturbations in a bouncing universe

“…(2.16) are negative, and including also a radiation fluid, one recovers the prototypical bouncing model already discussed in Ref. [13], which we shall discuss later on in Sec. 4.2.…”

“…There we show explicitly that, although presenting the abovementioned divergences in the adiabatic fluctuations, the equations governing the Bardeen potential and entropy fluctuations, when taken together without any adiabatic condition, yield a perfectly regular fourth order equation for the full Bardeen potential, which is equal to the one obtained in Ref. [13], whose solutions and derivatives must be regular at any time, including at the NEC transition. This reinforces the idea that there is no problem in defining entropy fluctuations in such bouncing models, but that we cannot neglect them around the NEC transition point.…”

“…in 4.2, we restrict ourselves to the particular case of a flat universe filled with a negative energy stiff matter and radiation, or, in other words, the situation equivalent to the case presented in Ref. [13]. There we show explicitly that, although presenting the abovementioned divergences in the adiabatic fluctuations, the equations governing the Bardeen potential and entropy fluctuations, when taken together without any adiabatic condition, yield a perfectly regular fourth order equation for the full Bardeen potential, which is equal to the one obtained in Ref.…”

“…It is worth pointing out that in some improvements of the regular bouncing models, not necessarily relying on general relativity at all times, perturbations may even be made scale-invariant [13], thus moving one step towards an alternative model of the Universe, namely one for which there is only a short period of accelerated expansion, which happens during the bouncing era following a contraction phase, in contrast with the relatively long period characteristic of usual inflationary scenarios.…”

“…More recently [13], we managed to obtain a model in which all perturbations are finite at all times, including the full Bardeen potential without imposing any adiabatic condition, by considering the case of a two fluids bouncing Universe, one of the fluids described by a scalar field.…”