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