Cosmological Perturbation Theory for streams of relativistic particles

TL;DR

This paper develops detailed equations for streams of relativistic particles within Cosmological Perturbation Theory, extending initial condition setups to different gauges and analyzing invariance properties in both linear and nonlinear regimes.

Contribution

It extends the formulation of relativistic particle streams to the Synchronous gauge and analyzes invariance properties, including the extended Galilean invariance, in nonlinear regimes.

Findings

Momentum field remains potential at subhorizon scales

Extended Galilean invariance applies to relativistic streams

Subhorizon nonlinear motion equations derived and analyzed

Abstract

Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes, express the matter and momentum conservation. In this context we extend the setup of adiabatic initial conditions - that was initially performed in the Conformal Newtonian gauge - to the Synchronous gauge. The subhorizon limit of the nonlinear motion equations written in a generic perturbed Friedmann-Lema\^{i}tre metric is then derived and analyzed. We show in particular that the momentum field $P_{i}(x)$ is always potential in the linear regime and remains so at subhorizon scales in the nonlinear regime. Finally the equivalence principle is exploited to highlight invariance properties satisfied by such a system of equations, extending that known for streams of non-relativistic particles, namely the extended Galilean invariance.