We consider the cosmological production of fermionic dark matter during inflation and a post-inflationary radiation dominated era. This fermion \emph{only interacts gravitationally}, has a mass $m$ much smaller than the Hubble scale during inflation (but is otherwise arbitrary) and is in its Bunch-Davies vacuum state during inflation. We focus on superhorizon modes at the end of inflation, and assume instantaneous reheating. We obtain the full energy momentum tensor discussing its renormalization, and show that the contribution from particle production is of the kinetic-fluid form near matter-radiation equality. We find \emph{exactly} the distribution function of produced particles $|B(k)|^2=\frac{1}{2}\Big[1-(1-e^{-\frac{k^2}{2mT_H}})^{1/2}\Big]$ which exhibits an " emergent temperature" $T_H=H_0\sqrt{Ω_R}\simeq 10^{-36}(\mathrm{eV})$. The abundance of the produced particles $Ω_{pp}$ is very similar to that of a non-relativistic degree of freedom thermalized at temperature $T_H$, $Ω_{pp} \propto m \, (m\,T_H)^{3/2}\simeq \big(m/10^8\mathrm{GeV})\big)^{5/2}$ and "cold" equation of state $w(a) \simeq (T_H/m a^2)$, both dominated by superhorizon modes at the end of inflation. We discuss subtle aspects of isocurvature perturbations.
Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
Institute for Theoretical Physics, University of Münster（明斯特大学理论物理研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙粒子与宇宙学研究所（WPI））；Physics Faculty, Taras Shevchenko National University of Kyiv（基辅塔拉斯·舍甫琴科国立大学物理系）
