# Higgs inflation in metric and Palatini formalisms: Required suppression of higher dimensional operators

## TL;DR

This paper compares Higgs inflation's robustness to higher dimensional operators in metric and Palatini formalisms, revealing extreme sensitivity in the Palatini case due to lack of an attractor, posing challenges for model realization.

## Contribution

It demonstrates the differing sensitivities of Higgs inflation to higher dimensional operators in metric versus Palatini formalisms, highlighting the need for suppression in the latter.

## Key findings

- Inflation predictions are stable in metric formalism near the attractor.
- Palatini formalism predictions are highly sensitive to small higher dimensional operators.
- Absence of attractor in Palatini formalism causes extreme sensitivity to operators.

## Abstract

We investigate the sensitivity of Higgs(-like) inflation to higher dimensional operators in the nonminimal couplings and in the potential, both in the metric and Palatini formalisms. We find that, while inflationary predictions are relatively stable against the higher dimensional operators around the attractor point in the metric formalism, they are extremely sensitive in the Palatini one: for the latter, inflationary predictions are spoiled by $|\xi_4| \gtrsim 10^{-6}$ in the nonminimal couplings $(\xi_2 \phi^2 + \xi_4 \phi^4 + \cdots)R$, or by $|\lambda_6| \gtrsim 10^{-16}$ in the Jordan-frame potential $\lambda_4 \phi^4 + \lambda_6 \phi^6 + \cdots$ (both in Planck units). This extreme sensitivity results from the absence of attractor in the Palatini formalism. Our study underscores the challenge of realizing inflationary models with the nonminimal coupling in the Palatini formalism.