Flow in Cyclic Cosmology

TL;DR

This paper extends the inflationary flow hierarchy to cyclic cosmologies using a duality, enabling analysis of perturbations in contracting models like Ekpyrotic and Cyclic scenarios.

Contribution

It introduces a duality-based framework for applying inflationary flow equations to contracting cosmologies, including a new approximation for perturbation spectra.

Findings

Flow equations are invariant under the duality.

Derived a self-consistent approximation for perturbation spectra.

Reproduced known solutions like Wands' matter-dominated contraction and Adiabatic Ekpyrosis.

Abstract

In this paper, we use a known duality between expanding and contracting cosmologies to construct a dual of the inflationary flow hierarchy applicable to contracting cosmologies such as Ekpyrotic and Cyclic models. We show that the inflationary flow equations are invariant under the duality and therefore apply equally well to inflation or to cyclic cosmology. We construct a self-consistent small-parameter approximation dual to the slow-roll approximation in inflation, and calculate the power spectrum of perturbations in this limit. We also recover the matter-dominated contracting solution of Wands, and the recently proposed Adiabatic Ekpyrosis solution.