Temperature fluctuations in an inhomogeneous diffusive fluid

TL;DR

This paper analyzes how metric perturbations in an expanding universe affect temperature fluctuations in a relativistic diffusive fluid, linking these to matter distribution and gravitational waves.

Contribution

It introduces a novel approach to relate temperature fluctuations to diffusion processes and tensor spectra in an inhomogeneous universe.

Findings

Derived a formula connecting temperature fluctuations with diffusion and tensor power spectra.

Explored the multipole expansion of temperature fluctuations considering diffusion effects.

Demonstrated that metric perturbations can be treated as temperature variations in the relativistic diffusion context.

Abstract

We discuss metric perturbations of the relativistic diffusion equation around the homogeneous Juttner equilibrium of massless particles in a homogeneous expanding universe. The metric perturbation describes matter distribution and the gravitational wave background in an inhomogeneous universe. We show that the lowest order perturbation can be treated as a variation of temperature. We derive a formula expressing temperature fluctuations in terms of the diffusion and tensor power spectrum. We discuss the multipole expansion of the fluctuations in the presence of diffusion.