Inflation in the Mixed Higgs-$R^2$ Model

TL;DR

This paper investigates a two-field inflation model combining $R^2$ gravity and the Higgs field, showing it can be effectively described as a single-field model with a modified sound speed and similar spectral index to known inflation models.

Contribution

It provides a detailed analysis of the power spectrum in a mixed Higgs-$R^2$ inflation model and demonstrates its effective single-field behavior with a modified sound speed.

Findings

The model's scalar spectral index matches $R^2$ and Higgs inflation predictions.

The Higgs field modifies the scalaron mass depending on the non-minimal coupling.

The model can be described as an effective single-field inflation with a modified sound speed.

Abstract

We analyze a two-field inflationary model consisting of the Ricci scalar squared ($R^2$) term and the standard Higgs field non-minimally coupled to gravity in addition to the Einstein $R$ term. Detailed analysis of the power spectrum of this model with mass hierarchy is presented, and we find that one can describe this model as an effective single-field model in the slow-roll regime with a modified sound speed. The scalar spectral index predicted by this model coincides with those given by the $R^2$ inflation and the Higgs inflation implying that there is a close relation between this model and the $R^2$ inflation already in the original (Jordan) frame. For a typical value of the self-coupling of the standard Higgs field at the high energy scale of inflation, the role of the Higgs field in parameter space involved is to modify the scalaron mass, so that the original mass parameter in the $R^2$ inflation can deviate from its standard value when non-minimal coupling between the Ricci scalar and the Higgs field is large enough.