Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field

TL;DR

This paper explores metric-affine gravity coupled to a scalar field, deriving an equivalent metric formulation and discussing implications for Higgs inflation, highlighting differences from traditional GR when matter is included.

Contribution

It constructs a scalar field model within metric-affine gravity, unifies various models, and derives an equivalent metric theory, providing insights into Higgs inflation implications.

Findings

Derived an equivalent metric formulation of scalar-tensor theory in metric-affine gravity.

Unified multiple models of gravity with scalar fields under a common framework.

Discussed potential implications for Higgs inflation scenarios.

Abstract

General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine gravity, which avoids any assumption about the vanishing of curvature, torsion or non-metricity. We use it to construct an action of a scalar field coupled non-minimally to gravity. It encompasses as special cases numerous previously studied models. Eliminating non-propagating degrees of freedom, we derive an equivalent theory in the metric formulation of GR. Finally, we give a brief outlook to implications for Higgs inflation.