Palatini formulation for gauge theory: implications for slow-roll inflation

TL;DR

This paper explores a Palatini-like formulation of gauge theories with independent gauge field and field strength variables, revealing that non-minimal couplings can stabilize the inflaton potential during slow-roll inflation, especially in Higgs inflation.

Contribution

It introduces a Palatini-inspired approach to gauge theories with non-minimal couplings, showing how this modifies the scalar sector and impacts inflationary potential stability.

Findings

Higher order inflaton potential terms do not spoil flatness in the modified theory.

The approach makes the effective potential more quadratic, aiding inflation.

It addresses the sensitivity of Higgs inflation to higher order terms in the Palatini formulation.

Abstract

We consider a formulation of gauge field theory where the gauge field $A_\alpha$ and the field strength $F_{\alpha\beta}$ are independent variables, as in the Palatini formulation of gravity. For the simplest gauge field action, this is known to be equivalent to the usual formulation. We add non-minimal couplings between $F_{\alpha\beta}$ and a scalar field, solve for $F_{\alpha\beta}$ and insert it back into the action. This leads to modified gauge field and scalar field terms. We consider slow-roll inflation and show that because of the modifications to the scalar sector, adding higher order terms to the inflaton potential does not spoil its flatness, unlike in the usual case. Instead they make the effective potential closer to quadratic. The modifications also solve the problem that Higgs inflation in the Palatini formulation is sensitive to higher order terms.