Analytic Approximations for Fermionic Preheating

Abstract

Non-thermal fermions can be produced non-perturbatively in the early universe during coherent oscillations of a scalar field. We explore fermion production in $\lambda {\varphi }^4$ inflation through this mechanism and analyze the momentum spectrum of the fermions produced, which depends on a coupling parameter $q$. For $q\gtrsim 0.01$, the main contribution to the total number density comes from an approximately half-filled Fermi sphere as a result of non-adiabaticity. For $q\lesssim 0.01$, we find that the major contributions instead come from resonance peaks at higher momentum values. We find a simple relation to predict the momentum values corresponding to resonance peaks for any $q$. We observe power-law behaviour for the total number density of fermions as a function of $q$ and find numerical approximations for the integrals describing the total number density. We find that it is proportional to $q^{1/2}$ for $q\lesssim 0.01$ and proportional to $q^{3/4}$ for $q\gtrsim 10$. If fermions produced by this mechanism make up the entirety of dark matter, we estimate lower bounds on their mass.

43 pages, 17 figures, v3: minor changes, typos corrected in Fig. 2 and Eq. 4.10, and appendices F and G added