Preheating and gravitational waves production in hybrid metric-Palatini model

In this study, we investigate the preheating era and the production of gravitational waves during this stage within the Higgs inflation hybrid metric-Palatini framework. In this setup, the Higgs field is supposed to be non-minimally coupled to the Palatini curvature through the coupling constant $\xi$. To study the evolution of the preheating process in terms of the reheating, characterized by the equation of state $\omega$, and inflationary parameters, we use a parameter $\delta$, which characterizes this process by relating the energy density at the end of inflation to the preheating one. We establish a link between gravitational wave density, preheating duration, and the spectral index by considering different specific values of the gravitational wave density spectrum. Additionally, we compare our results with the sensitivity curves of future experiments, analyzing the impact of preheating duration and the equation of state on the gravitational wave spectrum. We find that the Higgs hybrid metric-Palatini model can effectively explain both preheating and the production of gravitational waves during this era, with results that consistently agree with Planck data in the case where the coupling constant $\xi =10^{-4.1}$, the equation of state $\omega =1/4$ and the parameter $\delta =10^3$ or $\delta =10^7$.