Leptogenesis in exponential $f(R)$ gravity model

Abstract: We show that gravitational leptogenesis with dynamical $CPT$ breaking in an expanding universe can be reconciled with exponential $f(R)$ gravity models with axion as cold dark matter. For $L$ violating interactions, we consider both non-supersymmetric model with heavy right handed neutrino decay and supersymmetric model with sneutrino decay. For both the cases, we have shown that the required baryonis asymmetry could be obtained and also have shown the variation of decoupling temperature for lepton number violating interactions with $\beta$ parameter in exponential $f(R)$ gravity. Lepton number violating model parameters are contrained with $\beta$ through decoupling temperature. Upper bound on $\beta$ parameter is also obtained.