General relativistic non-ideal fluid equations for dark matter from a truncated cumulant expansion

TL;DR

This paper introduces a novel truncation scheme based on cumulant expansion for relativistic kinetic theory, deriving covariant equations to model non-ideal dark matter fluids in cosmology.

Contribution

It develops a new cumulant-based truncation method extending the moment approach, resulting in a covariant, hyperbolic system for relativistic non-ideal fluids.

Findings

Derived evolution equations for dark matter using cumulant expansion.

Applied the method to a cosmological model with dynamic pressure.

Solved for the effective equation of state parameter over time.

Abstract

A new truncation scheme based on the cumulant expansion of the one-particle phase-space distribution function for dark matter particles is developed. Extending the method of moments in relativistic kinetic theory, we derive evolution equations which supplement the covariant conservation of the energy-momentum tensor and particle number current. Truncating the cumulant expansion we obtain a closed, covariant and hyperbolic system of equations which can be used to model the evolution of a general relativistic non-ideal fluid. As a working example we consider a Friedmann-Lema\^itre-Robertson-Walker cosmology with dynamic pressure and solve for the time evolution of the effective equation of state parameter.