The reheating constraints to natural inflation in Horndeski gravity

Chen-Hsu Chien , Seoktae Koh, and Gansukh Tumurtushaa 2022 Eur. Phys. J. C  268 

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 Δ">Δ, mainly due to the suppressed tensor-to-scalar ratio. To be consistent with the data at the 1σ">1σ (68%">68% confidence) level, a slightly longer natural inflation with Nk≳60">Nk60 e-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 Nre">Nre, temperature Tre">Tre, and equation-of-state ωre">ωre 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 Nk">Nk. If reheating occurs instantaneously for which Nre=0">Nre=0 and ωre=1/3">ωre=1/3, the duration of natural inflation is about Nk≃57">Nk57 e-folds, where the exact value is less sensitive to the model parameter Δ">Δ compatible with the CMB data. The duration of natural inflation is longer (or shorter) than Nk≃57">Nk57 e-folds for the equation of state larger (or smaller) than 1/3 hence Nre≠0">Nre0. The maximum temperature at the end of reheating is Tremax≃3×1015">Tmaxre3×10^15 GeV, which corresponds to the instantaneous reheating. The low reheating temperature, as low as a few MeV, is also possible when ωre">ωre is closer to 1/3.