The reheating constraints to natural inflation in Horndeski gravity

Abstract

For the subclass of Horndeski theory of gravity, we investigate the effects of reheating on the predictions of natural inflation. In the presence of derivative self-interaction of a scalar field and its kinetic coupling to the Einstein tensor, the gravitational friction to inflaton dynamics is enhanced during inflation. As a result, the tensor-to-scalar ratio r is suppressed. We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter varDelta , mainly due to the suppressed tensor-to-scalar ratio. To be consistent with the data at the 1sigma (68% confidence) level, a slightly longer natural inflation with N_kgtrsim 60e-folds, longer than usually assumed, is preferred. Since the duration of inflation, for any specific inflaton potential, is linked to reheating parameters, including the duration N_{re}, temperature T_{re}, and equation-of-state omega _{re} parameter during reheating, we imposed the effects of reheating to the inflationary predictions to put further constraints. The results show that reheating consideration impacts the duration of inflation N_k. If reheating occurs instantaneously for which N_{re}=0 and omega _{re}=1/3, the duration of natural inflation is about N_ksimeq 57e-folds, where the exact value is less sensitive to the model parameter varDelta compatible with the CMB data. The duration of natural inflation is longer (or shorter) than N_ksimeq 57e-folds for the equation of state larger (or smaller) than 1/3 hence N_{re}ne 0. The maximum temperature at the end of reheating is T_{re}^text {max}simeq 3times 10^{15} GeV, which corresponds to the instantaneous reheating. The low reheating temperature, as low as a few MeV, is also possible when omega _{re} is closer to 1/3.