Velocity of sound in the relic photon sea

TL;DR

This paper calculates the velocity of sound in the cosmic relic photon gas using thermodynamics and explores the potential formation of Mach cones by high-energy particles moving faster than this sound speed.

Contribution

It provides a theoretical derivation of the sound velocity in relic photon gases across different dimensions and discusses implications for cosmic phenomena like Mach cones.

Findings

Derived spectral form for n-dimensional blackbody

Calculated sound velocity in 1D, 2D, and 3D photon gases

Discussed the possibility of Mach cone formation in cosmology

Abstract

We determine the velocity of sound in the blackbody gas of photons and in the gas of relic photons. Derivation is based on the thermodynamic theory of the photon gas and the Einstein relation between energy and mass. The spectral form for the n-dimensional blackbody is derived. The 1D, 2D and 3D blackbody radiation is specified. It is mentioned the possibility of creation of the Mach cone in case that the high energy cosmical particles moves with the speed greater than the velocity of sound in cosmical relic photon sea. Key words: Sound, elasticity, thermodynamics, blackbody, relic photons, Mach's cone.