Thermal leptogenesis in $f(R)$ cosmology

The cosmological consequences of $f(R)$ gravity are reviewed in the framework of thermal leptogenesis. In $f(R)$ cosmology the expansion laws of the Universe are modified with respect to the standard cosmology, which also changes the thermal history of particles. In these cosmological scenarios it turns out that the condition for the out-of-equilibrium decay of the lightest heavy neutrino gives rise to a modulated upper bound on the lightest light neutrino mass, i.e. ${\tilde{m}}_1\lesssim {10}^{-3}A(T=M_1)\mathrm{eV}$, where $A(T)$ is the ratio between the expansion rates of the Universe evaluated in $f(R)$ cosmology and in standard cosmology, and $M_1$ is the lightest heavy neutrino mass. This factor can be parametrized in terms of the temperature $T$ as $A(T)=(T/T_{*}{)}^p$, where $T_{*}$ is the transition temperature at which the expansion law in $f(R)$ cosmology deviates from the standard one, and $p$ is related to the parameters characterizing the $f(R)$ model under consideration. Results imply that if $A\gg 1$ then the thermal leptogenesis scenario can accommodate the case of a degenerate mass spectrum of the light neutrinos (for a low enough transition temperature), which is otherwise impossible with standard cosmology. In our analysis we consider $f(R)$ models of the form $f(R)=R+\alpha R^n$.