Higgs inflation and higher-order gravity in Palatini formulation

TL;DR

This paper investigates the impact of higher-order curvature terms on Higgs inflation within the Palatini formulation, revealing that scalar perturbations remain unaffected while tensor perturbations are suppressed.

Contribution

It introduces a novel analysis of Higgs inflation with higher-order curvature terms in the Palatini formulation, showing tensor spectrum suppression without affecting scalar spectrum.

Findings

Scalar perturbation spectrum remains unchanged.

Tensor perturbation spectrum is suppressed.

Higher-order curvature terms do not introduce new degrees of freedom.

Abstract

We study how higher-order gravity affects Higgs inflation in the Palatini formulation. We first review the metric and Palatini formulations in comparative manner and discuss their differences. Next cosmic inflation driven by a scalar field and inflationary observables are discussed. After this we review the Higgs inflation and compute the inflationary observables both in the metric and Palatini formulations. We then consider adding higher-order terms of the curvature to the action. We derive the equations of motion for the most general action quadratic in the curvature that does not violate parity in both the metric and Palatini formulations. Finally we present a new result. We analyse Higgs inflation in the Palatini formulation with higher-order curvature terms. We consider a simplified scenario where only terms constructed from the symmetric part of the Ricci tensor are added to the action. This implies that there are no new gravitational degrees of freedom, which makes the analysis easier. As a new result we found out that the scalar perturbation spectrum is unchanged, but the tensor perturbation spectrum is suppressed by the higher-order curvature couplings.