# Minimal Higgs inflation with an $R^2$ term in Palatini gravity

## TL;DR

This paper investigates Higgs inflation within Palatini gravity extended by an $R^2$ term, finding it can act as the inflaton but with spectral index predictions in tension with Planck data, though tensor-to-scalar ratio can be adjusted.

## Contribution

It corrects previous studies on Higgs inflation with an $R^2$ term in Palatini gravity and provides updated predictions for inflationary observables.

## Key findings

- Higgs can serve as the inflaton in this setup.
- Predicted spectral index $n_s \,\simeq 0.941$ is in tension with Planck.
- Tensor-to-scalar ratio $r$ can be suppressed and made compatible with data.

## Abstract

It has recently been suggested that the Standard Model Higgs boson could act as the inflaton while minimally coupled to gravity - given that the gravity sector is extended with an $\alpha R^2$ term and the underlying theory of gravity is of Palatini, rather than metric, type. In this paper, we revisit the idea and correct some shortcomings in earlier studies. We find that in this setup the Higgs can indeed act as the inflaton and that the tree-level predictions of the model for the spectral index and the tensor-to-scalar ratio are $n_s\simeq 0.941$, $r\simeq 0.3/(1+10^{-8}\alpha)$, respectively, for a typical number of e-folds, $N=50$, between horizon exit of the pivot scale $k=0.05\, {\rm Mpc}^{-1}$ and the end of inflation. Even though the tensor-to-scalar ratio is suppressed compared to the usual minimally coupled case and can be made compatible with data for large enough $\alpha$, the result for $n_s$ is in severe tension with the Planck results. We briefly discuss extensions of the model.