Leptogenesis in exponential $f(R)$ gravity model

We show that gravitational leptogenesis with dynamical $CPT$ breaking in an expanding universe can be reconciled with the exponential $f(R)$ gravity model, which introduces only one additional parameter $\beta$ compared to the standard $\Lambda$CDM cosmology. This model incorporated axions as cold dark matter. For $L$ violating interactions, we consider both a non-supersymmetric model with heavy right-handed neutrino decay and a supersymmetric model with sneutrino decay. For both cases, we have shown that the required baryonic asymmetry could be obtained. We have also shown the variation of decoupling temperature for lepton number violating interactions with the $\beta$ parameter in exponential $f(R)$ gravity. Lepton number-violating model parameters are constrained with the $\beta$ through the decoupling temperature. An upper bound on the $\beta$ parameter of the exponential $f(R)$ gravity is also obtained.