Preheating of Fermions

Abstract

In inflationary cosmology, the particles constituting the Universe are created after inflation in the process of reheating due to their interaction with the oscillating inflaton field. In the bosonic sector, the leading channel of particle production is the non-perturbative regime of parametric resonance, preheating, during which bosons are created exponentially fast. Pauli blocking prohibits the unbounded creation of fermions. For this reason, it has been silently assumed that the creation of fermions can be treated with perturbation theory for the decay of individual inflatons. We consider the production of fermions interacting with the coherently oscillating inflatons. We find that the actual particle production occurs in a regime of the parametric excitation of fermions, leading to preheating of fermions. Fermion preheating differs significantly from the perturbative expectation. It turns out that the number density of fermions varies periodically with time. The total number of fermions quickly saturates to an average value within a broad range of momenta $\propto q^{1/4}$, where $q$ is the usual resonance parameter. The resonant excitation of fermions may affect the transfer inflaton energy, estimations of the reheating temperature, and the abundance of superheavy fermions and gravitinos. Back in the bosonic sector, outside of the parametric resonance bands there is an additional effect of parametric excitation of bosons with bounded occupation number in the momentum range $\propto q^{1/4}$.

Figures (6)

• Figure 1: The occupation number $n_k$ in $\lambda \phi^4$-inflation as a function of time $\tau$ (in units of $T$) for $q \equiv {h^2 \over \lambda} = 10^{-4}$ (lower), $1$ (middle on right), and $100$ (upper on right) and $\kappa^2 = 0.18, 1.11$, and $11.9$, respectively. The period of the modulation $\pi \over {\nu_k}$ (see Eq. (\ref{['average']})) is about $88$, $20$ and $22$ (in units of $T$) accordingly.
• Figure 2: The envelope functions $F_k$ showing the bands of fermion resonance excitation in $\lambda \phi^4$-inflation for $q \equiv {h^2 \over \lambda} = 10^{-4}, 10^{-2}$, and $1.0$ (the narrowest to broadest band, respectively). The band in the case $q = 10^{-2}$ already deviates considerably from the perturbative expectation.
• Figure 3: The resonance excitation band of fermions in $\lambda \phi^4$-inflation for $q \equiv {h^2 \over \lambda} = 1.0$. The heavy line shows the envelope $F_k$ of maximum occupation number calculated from Eq. (\ref{['15']}). The light curve is the actual occupation number $n_k$ of each mode, calculated from Eq. (\ref{['average']}), after $10$ background oscillations.
• Figure 4: As in Fig. 3, the resonance excitation band in $\lambda \phi^4$-inflation for $q \equiv {h^2 \over \lambda} = 100.0$. The heavy line shows the envelope $F_k$. The light curve is the actual occupation number of each mode $n_k$ after $10$ background oscillations.
• Figure 5: The $\log$ of the period of modulation ${\pi \over \nu_k}$ (in units of $T$) as a function of $\kappa^2$ for $q \equiv {h^2 \over \lambda} = 10^{-4}, 10^{-2}$, and $1.0$ for the light, dotted, and heavy curves respectively.