On Inflation and Reheating Features in the Higgs-$R^2$ Model

Abstract: We investigated inflation in the Higgs-$R^2$ model and assumed the trajectory to follow a single-field approximation called minimal two-field mode. Using this approximation, we tried to constrain the Higgs' non-minimal coupling $\xi$. During inflation, we investigated the effect of $\xi$ on the non-gaussianity. We found that $\xi$ could not provide the large non-gaussianity. In this paper, we divided the preheating stage to be quadratic regime and quartic regime. During the quadratic regime, the gauge bosons' production is the most dominant. However, it could not drain the whole inflaton's energy. Thus, we introduced a dark matter candidate with a large coupling that could drain the whole inflaton's energy. We also found that if $\xi<4.2$, the oscillation on the quadratic regime continued to the quartic regime. The reheating temperature obtained by this mode can be reached to be $\sim 10^{10}$ GeV and strongly depends on the remaining inflaton's energy density. On contrary, if $\xi>4.2$, the oscillation only happens at the quadratic regime. As we assumed the Pauli exclusion principle does exist during the quadratic regime, the instant decay of gauge bosons to fermions is restricted. Hence we expected, the reheating temperature to be low for about $\sim 10^9$ GeV.