Nonminimally-coupled warm Higgs inflation: Metric vs. Palatini Formulations

In this work, we study the non-minimally-coupled Higgs model in the context of warm inflation scenario on both metric and Palatini approaches. We particularly consider a dissipation parameter of the form $\Gamma=C_{T}T$ with $C_{T}$ being a coupling parameter and focus only on the strong regime of the interaction between inflaton and radiation fluid. We compute all relevant cosmological parameters and constrain the models using the observational Planck 2018 data. We discover that the $n_s$ and $r$ values are consistent with the observational bounds. Having used the observational data, we constrain a relation between $\xi$ and $\lambda$ for the non-minimally-coupled warm Higgs inflation in both metric and Palatini cases. To produce $n_s$ and $r$ in agreement with observation, we find that their values are two orders of magnitude higher than those of the usual (cold) non-minimally-coupled Higgs inflation.