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

TL;DR

This paper investigates how non-minimal coupling affects inflationary predictions in Palatini gravity, focusing on Higgs and Coleman-Weinberg potentials with a non-zero vacuum expectation value, aligning models with recent observational data.

Contribution

It analyzes inflationary parameters for Higgs and Coleman-Weinberg potentials with non-zero VEV in Palatini gravity, identifying parameter regions consistent with observations.

Findings

Inflationary predictions depend on the non-minimal coupling $\xi$ and VEV $v$.

Linear inflation behavior emerges at $\xi v^2=1$ in Coleman-Weinberg potential.

Preferred $\xi$ values vary with $v$ to match observational constraints.

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.