Cosmologically degenerate fermions

Dark matter (DM) with a mass below few keV must have phase space distribution that differs substantially from the Standard Model particle thermal space: otherwise, it will free stream out of cosmic structures as they form. We observe fermionic DM $\ensuremath{\psi}$ in this range non-negligible momentum early Universe, even total absence kinetic energy. This is because fermions were inevitably more dense at higher redshifts, and thus experienced Pauli degeneracy pressure. They fill up lowest-momentum states, such typical fermion gains $\ensuremath{\sim}\mathcal{O}({p}_{F})$ can exceed its ${m}_{\ensuremath{\psi}}$. find simple relation between ${m}_{\ensuremath{\psi}}$, current fraction ${f}_{\ensuremath{\psi}}$ cold energy density light fermions, redshift which relativistic. Considering impacts transition nonrelativistic relativistic behavior revealed by constraints on $\mathrm{\ensuremath{\Delta}}{N}_{\mathrm{eff}}$ power spectrum, we derive qualitatively new bounds ${f}_{\ensuremath{\psi}}\ensuremath{-}{m}_{\ensuremath{\psi}}$ plane. also improve existing for ${f}_{\ensuremath{\psi}}=1$ to be ${m}_{\ensuremath{\psi}}\ensuremath{\ge}2\text{ }\text{ }\mathrm{keV}$. remark implications direct detection suggest models dark sectors may give rise cosmologically degenerate fermions.