Large Field Polynomial Inflation in Palatini $f(R,φ)$ Gravity

Abstract: In this paper, we employ the Palatini formalism to investigate the dynamics of large-field inflation using a renormalizable polynomial inflaton potential in the context of $f(R,\phi)$ gravity. Assuming instant reheating, we make a comparative analysis of large-field polynomial inflation (PI). We first consider the minimal and non-minimal coupling of inflaton in $R$ gravity, and then we continue with the minimally and non-minimally coupled inflaton in $f(R,\phi)$ gravity. We scan the parameter space for the inflationary predictions ($n_s$ and $r$) consistent with the Planck and BICEP/Keck 2018 results as well as the sensitivity forecast of the future CMB-S4 and depict the compliant regions in the $\phi_0-\beta$ plane where $\phi_0$ and $\beta$ are two parameters of polynomial inflation model which control the saddle point of the potential and the flatness in the vicinity of this point respectively. We find that a substantial portion of the parameter space aligns with the observational data.