Bose and Fermi gases in the early universe with self-gravitational effect

TL;DR

This paper investigates the impact of self-gravity on the thermodynamic properties of Bose and Fermi gases in the early universe, providing new equations of state and confirming the negligible effect on cosmic evolution.

Contribution

It introduces new grand canonical partition functions for self-gravitating quantum gases and analyzes their effects during key early universe epochs.

Findings

Self-gravitational effects are negligible, altering state constants by less than 10^{-78}.

New EoSs reveal distinct behaviors for relativistic and non-relativistic gases under gravity.

Clarifies the thermal evolution of the primordial universe, aiding in testing gravity and inflation models.

Abstract

We study the self-gravitational effect on the equation of state (EoS) of Bose and Fermi gases in thermal equilibrium at the end of reheating, the period after quark-hadron transition and before Big Bang Nucleosynthesis (BBN). After introducing new grand canonical partition functions based on the work of Uhlenbeck and Gropper, we notice some interesting features of the newly developed EoSs with distinct behaviors of relativistic and non-relativistic gases under self-gravity. The usual negligence of the self-gravitational effect when solving the background expansion of the early universe is justified with numerical results, showing the magnitude of the self-gravitational modification of the state constant to be less than $O(10^{-78})$. This helps us to clarify the background thermal evolution of the primordial patch. Such clarification is crucial in testing gravity theories, evaluating inflation models and determining element abundances in BBN.