Geometric phases and cyclic isotropic cosmologies

TL;DR

This paper investigates the evolution of scalar field modes in a cyclic universe model, revealing that particle production and Berry phases carry information across bounces, with implications for quantum cosmology.

Contribution

It introduces a toy model of cyclic cosmology to analyze scalar field dynamics, highlighting the role of Berry phases in information transfer between cycles.

Findings

Scalar field modes exhibit particle production in cyclic cosmology.

The Berry phase remains non-zero across bounces, indicating information transfer.

Quantum regime shows significant particle content and non-zero Berry phase.

Abstract

In the present paper we study the evolution of the modes of a scalar field in a cyclic cosmology. In order to keep the discussion clear, we study the features of a scalar field in a toy model, a Friedman-Robertson-Walker universe with a periodic scale factor, in which the universe expands, contracts and bounces infinite times, in the approximation in which the dynamic features of this universe are driven by some external factor, without the backreaction of the scalar field under study. In particular, we show that particle production exhibits features of the cyclic cosmology. Also, by studying the Berry phase of the scalar field, we show that contrarily to what is commonly believed, the scalar field carries information from one bounce to another in the form of a global phase which occurs to be generically non-zero. {The Berry phase is then evaluated numerically in the case of the effective Loop Quantum Cosmology closed Universe. We observe that Berry's phase is nonzero, but that in the quantum regime the particle content is non-negligible.