Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies

TL;DR

This paper proves that small non-linear perturbations in expanding flat homogeneous cosmologies decay exponentially over time, with exceptions for very stiff fluids like pure radiation.

Contribution

It demonstrates exponential decay of small non-linear perturbations in a broad class of cosmological models, excluding very stiff fluids.

Findings

Small non-linear perturbations decay exponentially during expansion.

The decay result applies to many perfect fluid equations of state.

Pure radiation case does not exhibit exponential decay.

Abstract

It is shown that during expanding phases of flat homogeneous cosmologies all small enough non-linear perturbations decay exponentially. This result holds for a large class of perfect fluid equations of state, but notably not for very ``stiff'' fluids as the pure radiation case.