Scale Invariance via a Phase of Slow Expansion

TL;DR

This paper demonstrates that a scale-invariant spectrum of curvature perturbations can be generated during a slowly expanding universe with a rapidly changing equation of state, extending previous contracting models to expanding scenarios.

Contribution

It generalizes the adiabatic ekpyrotic mechanism to include expanding backgrounds, showing both expanding and contracting phases as attractors for scale-invariant perturbation generation.

Findings

Both expanding and contracting scenarios are dynamical attractors.

A finite range of scale-invariant modes can be generated within perturbation theory.

The expanding scenario has a broader basin of attraction.

Abstract

We consider a cosmological scenario in which a scale-invariant spectrum of curvature perturbations is generated by a rapidly-evolving equation of state on a slowly expanding background. This scenario generalizes the "adiabatic ekpyrotic" mechanism proposed recently in arXiv:0910.2230. Whereas the original proposal assumed a slowly contracting background, the present work shows that the mechanism works equally well on an expanding background. This greatly expands the realm of broader cosmological scenarios in which this mechanism can be embedded. We present a phase space analysis and show that both the expanding and contracting versions of the scenario are dynamical attractors, with the expanding branch having a broader basin of attraction. In both cases, a finite range of scale invariant modes can be generated within the regime of validity of perturbation theory.