Fermion reheating with a quartic inflaton potential

TL;DR

This paper addresses reheating after inflation when the inflaton resides in a quartic minimum, focusing on fermion production via Yukawa couplings and the competing effects of inflaton self-resonance and fragmentation. It combines non-perturbative (Heisenberg/Bogoliubov) and perturbative (Boltzmann) techniques to study fermion production both before and after fragmentation, including Pauli blocking and kinematic suppression. The main findings show that pre-fragmentation reheating requires relatively large Yukawa couplings ($y \gtrsim 0.2$), while smaller couplings lead to fragmentation before complete reheating, with post-fragmentation Pauli blocking further suppressing production. Altogether, the work places conservative bounds on fermionic reheating in quartic-inflaton models and highlights the need for additional channels or rapid thermalization to achieve BBN-relevant temperatures.

Abstract

Any viable inflationary model must account for reheating of the universe prior to the onset of primordial nucleosynthesis. In this work, we study the reheating mechanism for an inflaton field with a quartic minimum, assuming that the main particle production channel corresponds to the decay into a pair of spin 1/2 fermions via Yukawa-like interactions. On top of its decays, the self-interaction of the inflaton sources the resonant growth of inflaton inhomogeneities, leading to its eventual fragmentation, unless reheating is completed in a shorter timescale. By means of a combination of non-perturbative (Heisenberg/Bogoliubov) and perturbative (Boltzmann) methods, we find that for Yukawa couplings $y\gtrsim 10^{-8}$ parametric resonance, kinematic blocking, and Pauli suppression effects cannot be ignored to estimate the fermion energy density during reheating. Reheating prior to nucleosynthesis requires couplings above this threshold, and in particular, reheating occurring before fragmentation is only possible for $y\gtrsim 0.2$.

Figures (10)

• Figure 1: Left: Floquet chart for Hill's equation (\ref{['eq:hills']}). The gray bands show the regions of exponential growth of inflaton fluctuations. Right: Time dependence of the total inflaton energy density (blue), the energy density of the inflaton inhomogeneities (orange), and the energy density of the homogeneous component (green) for the quartic T-model (\ref{['eq:Tquart']}). For $a/a_{\rm end}<10^2$ these energies are computed using the linear approximation, while at later times lattice methods are utilized.
• Figure 2: Left: The phase space distribution (PSD) for the inflaton inhomogeneities $\delta\phi$ evaluated at a selection of scale factors, during and after the fragmentation process. Right: The comoving number density of the inflaton fluctuations as a function of the scale factor. We assume here that reheating ends at $a_{\rm reh}\gg 10^{3}a_{\rm end}$.
• Figure 3: Kinematic suppression factor for the effective inflaton-fermion coupling (\ref{['eq:yeff']}), as a function of the mass ratio $\mathcal{R}$.
• Figure 4: Left: Pre-fragmentation fermion PSD (\ref{['eq:psdnp']}) evaluated at different times (see legend) for the Yukawa coupling $y=10^{-8}$. The position of the first five peaks predicted by the Boltzmann approximation (\ref{['eq:Boltzpeaks']}) are shown as the vertical dashed gray lines. Right: Exact pre-fragmentation energy density of $\psi$ obtained from the integration of the PSD shown in the left panel (black, continuous), compared to the perturbative Boltzmann approximation (blue, dotted). For this case $\mathcal{R}\simeq0$ and kinematic suppression is negligible. For reference we also show the energy density of the inflaton condensate (red, continuous), and the energy density for the case of an axial coupling with strength $y_5=10^{-8}$ (dashed, orange).
• Figure 5: As in Fig. \ref{['fig:1e-8']}, the fermion PSD before fragmentation, for a Yukawa coupling $y=10^{-6}$ (left), and a comparison of different approximations to $\rho_{\psi}$ (right).