A Hydrodynamical Approach to CMB mu-distortions

TL;DR

This paper provides a comprehensive analysis of the physical processes involved in the generation and evolution of mu-type spectral distortions in the cosmic microwave background, enhancing understanding of small-scale primordial perturbations.

Contribution

It systematically discusses all relevant physical phenomena and confirms previous estimates, including relativistic corrections, while also exploring additional subleading effects.

Findings

Main results agree with previous estimates.

Relativistic corrections account for a factor of 3/4.

Calculated transfer function for mu-distortions from mu-era to present.

Abstract

Spectral distortion of the cosmic microwave background provides a unique opportunity to probe primordial perturbations on very small scales by performing large-scale measurements. We discuss in a systematic and pedagogic way all the relevant physical phenomena involved in the production and evolution of the mu-type spectral distortion. Our main results agree with previous estimates (in particular we show that a recently found factor of 3/4 arises from relativistic corrections to the wave energy). We also discuss several subleading corrections such as adiabatic cooling and the effects of bulk viscosity, baryon loading and photon heat conduction. Finally we calculate the transfer function for mu-distortions between the end of the mu-era and now.