Non-thermal cosmic neutrino background

We point out that, for Dirac neutrinos, in addition to the standard thermal cosmic neutrino background (C$\nu$B) there could also exist a non-thermal neutrino background with comparable number density. As the right-handed components are essentially decoupled from the thermal bath of standard model particles, relic neutrinos with a non-thermal distribution may exist until today. The relic density of the non-thermal (nt) background can be constrained by the usual observational bounds on the effective number of massless degrees of freedom $N_\mathrm{eff}$, and can be as large as $n_{\nu_{\mathrm{nt}}}\lesssim 0.5\,n_\gamma$. In particular, $N_\mathrm{eff}$ can be larger than 3.046 in the absence of any exotic states. Non-thermal relic neutrinos constitute an irreducible contribution to the detection of the C$\nu$B, and, hence, may be discovered by future experiments such as PTOLEMY. We also present a scenario of chaotic inflation in which a non-thermal background can naturally be generated by inflationary preheating. The non-thermal relic neutrinos, thus, may constitute a novel window into the very early universe.