Higgs inflation with loop corrections in the Palatini formulation

TL;DR

This paper compares Higgs inflation in metric and Palatini formulations, showing that loop corrections and gravitational degrees of freedom significantly affect inflationary observables, which can help distinguish between these formulations.

Contribution

It provides a detailed comparison of Higgs inflation with loop corrections in metric and Palatini formulations, highlighting observable differences in inflationary predictions.

Findings

Palatini formulation suppresses tensor-to-scalar ratio r compared to metric.

Inflationary observables like n_s and r can distinguish gravitational degrees of freedom.

Non-detection of r does not rule out Higgs inflation, only the metric variant.

Abstract

We compare Higgs inflation in the metric and Palatini formulations of general relativity, with loop corrections are treated in a simple approximation. We consider Higgs inflation on the plateau, at a critical point, at a hilltop and in a false vacuum. In the last case there are only minor differences. Otherwise we find that in the Palatini formulation the tensor-to-scalar ratio is consistently suppressed, spanning the range $1\times10^{-13}<r<7\times10^{-5}$, compared to the metric case result $2\times10^{-5}<r<0.2$. Even when the values of $n_s$ and $r$ overlap, the running and running of the running are different in the two formulations. Therefore, if Higgs is the inflaton, inflationary observables can be used to distinguish between different gravitational degrees of freedom, in this case to determine whether the connection is an independent variable. Non-detection of $r$ in foreseeable future observations would not rule out Higgs inflation, only its metric variant. We conclude that in order to fix the theory of Higgs inflation, not only the particle physics UV completion but also the gravitational degrees of freedom have to be explicated.