Gravitational effects on the Higgs field within the Solar System
  The Higgs mechanism predicts, apart from the existence of a new scalar boson,
the presence of a constant Higgs field that permeates all of space. The vacuum
expectation value (VEV) of this field is affected by quantum corrections which
are mainly generated by the self-interactions and couplings of the Higgs field
to gauge bosons and heavy quarks. In this work we show that gravity can affect,
in a non-trivial way, these quantum corrections through the finite parts of the
one-loop contributions to the effective potential. In particular, we consider
the corrections generated by the Standard Model Higgs self-interactions in
slowly-varying weak gravitational backgrounds. The obtained results amount to
the existence of non-negligible inhomogeneities in the Higgs VEV. Such
inhomogeneities translate into spatial variations of the particle masses, and
in particular of the proton-to-electron mass ratio. We find that these Higgs
perturbations in our Solar System are controlled by the Eddington parameter,
and are absent in pure General Relativity. Yet, they may be present in modified
gravity theories. This predicted effect may be constrained by atomic clocks or
high-resolution spectroscopic measurements, which could allow to improve
current limits on modifications of Einstein's gravity.
