Preheating of massive fermions after inflation: analytical results

Non-perturbative production of fermions after chaotic inflation has been the object of several studies in the very recent past. However, the results in the most interesting case of production of massive fermions in an expanding Universe were so far known only numerically. We provide very simple and readable analytical formulae, both for the spectra of the created fermions and for their total energy density. Their derivation is closely related to the one adopted for bosons and exploits the fact that the production occurs during very short intervals of non-adiabatical change of the fermionic frequency. Our formulae show the presence of resonance bands if the expansion of the Universe is neglected, and their disappearance when the latter is included. As in the bosonic case, this last effect is due to the stochastic character that the expansion gives to the whole process. Backreaction is considered in the last part of the work. All our analytical results are in excellent agreement with the previous numerical ones in the regime of validity of the latter. However, a more accurate scaling for the energy density of the produced fermions is here found.