Bouncing models with a cosmological constant

TL;DR

This paper investigates how a cosmological constant influences the evolution of cosmological perturbations in bouncing models, revealing modifications to the spectrum including oscillations and a slight red tilt.

Contribution

It introduces the effect of a cosmological constant on perturbations in bouncing cosmologies, highlighting changes in amplitude and spectral tilt.

Findings

Almost scale-invariant spectrum for w~0

Oscillations induced by the cosmological constant

Red-tilted spectrum for long wavelengths

Abstract

Bouncing models have been proposed by many authors as a completion, or even as an alternative to inflation for the description of the very early and dense Universe. However, most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role as it has today in accelerating our large Universe. In that case, its presence can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this paper, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and evaluate its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, which also contains a scalar field with a potential allowing background solutions with pressure and energy density satisfying p = w*rho, w being a constant. An initial adiabatic vacuum state can be set at the end of domination by the cosmological constant, and an almost scale invariant spectrum of perturbations is obtained for w~0, which is the usual result for bouncing models. However, the presence of the cosmological constant induces oscillations and a running towards a tiny red-tilted spectrum for long wavelength perturbations.