Palatini Higgs and Coleman-Weinberg inflation with non-minimal coupling

Abstract

We present the impact of non-minimal coupling $\xi \phi^2 R$ on the inflationary parameters by taking into account the models of single-field inflation with the inflaton that has a non-zero vacuum expectation value ($v$) after the period of inflation in Palatini gravity. We discuss the well-known symmetry breaking type potentials, namely the Higgs potential and Coleman-Weinberg potential. We show the inflationary predictions of these potentials, for both $\phi>v$ and $\phi<v$ inflation, the regions in the $v-\xi$ plane for which the values of $n_s$ and $r$ are in agreement with the recent measurements. We also show the linear inflation behavior as a solution of Coleman-Weinberg potential for $\xi v^2=1$ limit. Finally, we take into account the inflationary predictions of Coleman-Weinberg potential for preferred $\xi$ values as a function of $v$ in Palatini formalism.