Parameter space of leptogenesis in polynomial inflation

Polynomial inflation is a very simple and well motivated scenario. A potential with a concave "almost" saddle point at field value phi=phi(0) fits well the cosmic microwave background (CMB) data and makes testable predictions for the running of the spectral index and the tensor to scalar ratio. In this work we analyze leptogenesis in the polynomial inflation framework. We delineate the allowed parameter space giving rise to the correct baryon asymmetry as well as being consistent with data on neutrino oscillations. To that end we consider two different reheating scenarios. (i) If the inflaton decays into two bosons, the reheating temperature can be as high as T-rh similar to 10(14) GeV without spoiling the flatness of the potential, allowing vanilla N1 thermal leptogenesis to work if T-rh> M-1 where N-1 is the lightest right-handed neutrino and M-1 its mass. Moreover, if the dominant decay of the inflaton is into Higgs bosons of the Standard Model, we find that rare three -body inflaton decays into a Higgs boson plus one light and one heavy neutrino allow leptogenesis even for T-rh> M-1 if the inflaton mass is of order 10(12) GeV or higher; in the polynomial inflation scenario this requires phi(0)greater than or similar to 2.5 MP. This novel mechanism of non -thermal leptogenesis is quite generic, since the coupling leading to the three -body final state is required in the type I see -saw mechanism. (ii) If the inflaton decays into two fermions, the flatness of the potential implies a lower reheating temperature. In this case inflaton decay to two N1 still allows successful non -thermal leptogenesis if phi(0) greater than or similar to 0.1 MP and T-rh greater than or similar to 10(6) GeV.