Thermodynamic equilibrium in the expanding universe

TL;DR

This paper demonstrates that a relativistic gas can achieve global thermodynamic equilibrium in an expanding universe under specific conditions involving a self-interacting force, extending previous understanding of equilibrium states.

Contribution

It introduces a new mechanism for equilibrium in an expanding universe through a self-interacting force, generalizing known conditions for ultrarelativistic matter.

Findings

Relativistic gas can be at global equilibrium with a self-interacting force.

Equilibrium conditions extend to any equation of state with 0 < p ≤ ρ/3.

Force-free limit recovers known ultrarelativistic matter equilibrium conditions.

Abstract

We show that a relativistic gas may be at ``global'' equilibrium in the expanding universe for any equation of state $0 < p \leq \rho /3$, provided that the gas particles move under the influence of a self-interacting, effective one-particle force in between elastic binary collisions. In the force-free limit we recover the equilibrium conditions for ultrarelativistic matter which imply the existence of a conformal timelike Killing vector.