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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 vacuumexpectation value (VEV) of this field is affected by quantum corrections whichare mainly generated by the self-interactions and couplings of the Higgs fieldto 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 theone-loop contributions to the effective potential. In particular, we considerthe corrections generated by the Standard Model Higgs self-interactions inslowly-varying weak gravitational backgrounds. The obtained results amount tothe existence of non-negligible inhomogeneities in the Higgs VEV. Suchinhomogeneities translate into spatial variations of the particle masses, andin particular of the proton-to-electron mass ratio. We find that these Higgsperturbations in our Solar System are controlled by the Eddington parameter,and are absent in pure General Relativity. Yet, they may be present in modifiedgravity theories. This predicted effect may be constrained by atomic clocks orhigh-resolution spectroscopic measurements, which could allow to improvecurrent limits on modifications of Einstein's gravity.

Gravitational effects on the Higgs field within the Solar System