On the Generation of a Scale-Invariant Spectrum of Adiabatic Fluctuations in Cosmological Models with a Contracting Phase

TL;DR

This paper introduces a new contracting cosmological model with a single scalar field that produces a scale-invariant spectrum of fluctuations, addressing limitations of previous models like Pre-Big-Bang and Ekpyrotic scenarios.

Contribution

A novel contracting background model with a single scalar field yielding a scale-invariant spectrum, and new solutions involving two scalar fields with exponential potentials.

Findings

A single scalar field model achieves scale-invariant fluctuations.

Matching contracting phase to expansion preserves scale invariance.

New multi-field solutions extend previous cosmological models.

Abstract

In Pre-Big-Bang and in Ekpyrotic Cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting (viewed in the Einstein frame). The backgrounds studied to date do not yield a scale invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model (neither of Pre-Big-Bang nor of the Ekpyrotic form) involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar field corresponds to cold matter. We demonstrate that if this contracting phase can be matched via a nonsingular bounce to an expanding Friedmann cosmology, the scale-invariance of the curvature fluctuations is maintained. We also find new background solutions for Pre-Big-Bang and for Ekpyrotic cosmology, which involve two scalar fields with exponential potentials with background values which are evolving in time. We comment on the difficulty of obtaining a scale-invariant spectrum of adiabatic fluctuations with background solutions which have been studied in the past.