Nearly Divergence of Correlation Length and Perturbation Spectrum in String Gas Cosmology

TL;DR

This paper explores how a nearly divergent correlation length at a phase transition in string gas cosmology can facilitate the generation of scale-invariant primordial perturbations, building on thermodynamic fluctuation mechanisms.

Contribution

It proposes that a nearly divergent correlation length at a phase transition enables the string gas mechanism to produce scale-invariant perturbations effectively.

Findings

Correlation length may diverge at phase transition

String gas mechanism can generate scale-invariant spectrum

Perturbation spectrum remains nearly scale-invariant

Abstract

Recently, it has been shown in Ref.[1] that the string thermodynamic fluctuation may lead to a scale invariant spectrum of scalar metric perturbation. However, its realization is still in study. In this note we suppose that the correlation length of metric perturbation, which is proportional to the sound speed, might be nearly divergent at the critical point of phase transition. In this case we find that the string gas mechanism responsible for the generation of primordial perturbation may be applied well.