Cosmological evolution of collisionless relativistic gases as dark matter

TL;DR

This paper models dark matter as a collisionless relativistic gas in a flat universe, deriving analytic expressions for its properties, implementing it in a Boltzmann code, and comparing with Planck data to constrain its parameters.

Contribution

It introduces a novel relativistic kinetic gas dark matter model with analytic solutions and tests its observational viability against cosmological data.

Findings

Small particle velocities are indistinguishable from standard cold dark matter.

Larger velocities with relativistic effects are constrained by observations.

The model is consistent with current cosmological measurements.

Abstract

We study a phenomenological dark matter model described as a collisionless relativistic kinetic gas in a spatially flat Friedmann-Lema\^itre-Robertson-Walker universe. After normalization to the observed present-day dark matter abundance, the model is fully specified by a single dimensionless parameter $\beta$, interpreted as the present particle velocity in units of the speed of light. The resulting energy density, pressure, and sound speed admit closed analytic expressions, interpolating between a radiation-like regime at early times and cold dark matter at late times. We implement the model in a modified version of the Boltzmann code CLASS and confront it with Planck 2018 CMB data. We find that sufficiently small values of $\beta$ are observationally indistinguishable from $\Lambda$CDM, while larger values inducing relativistic effects at early times are constrained. These results establish the consistency of the relativistic kinetic gas scenario with current cosmological observations.