Analytic Approximations for Fermionic Preheating

TL;DR

This paper derives analytic formulas for fermion production during preheating in the early universe, analyzing how the spectrum and density depend on coupling strength, with implications for dark matter.

Contribution

It provides new analytic approximations for fermion momentum spectra and total densities in fermionic preheating, including resonance peak predictions and scaling laws.

Findings

Fermion spectrum depends on coupling parameter q, with different dominant contributions for q above or below 0.01.

Analytic power-law relations for total fermion number density: proportional to q^{1/2} for q<0.01 and q^{3/4} for q>10.

Derived a simple relation to predict resonance peak momentum values for any q.

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 $\lambda\phi^{4}$ 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 also obtain analytic power-law approximations for the total number density of fermions and 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.