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