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Despite the enormous significance of the Higgs potential in the context ofthe Standard Model of electroweak interactions and in Grand Unified Theories,its ultimate origin is fundamentally unknown and must be introduced by hand inaccordance with the underlying gauge symmetry and the requirement ofrenormalizability. Here we propose a more physical motivation for the structureof the Higgs potential, which we link to gravity, and more specifically to anextended Brans-Dicke (BD) theory containing two interacting scalar fields. Oneof these fields is coupled to curvature as in the BD formulation, whereas theother is coupled to gravity both derivatively and non-derivatively through thecurvature scalar and the Ricci tensor. By requiring that the cosmologicalsolutions of the model are consistent with observations, we show that theeffective scalar field potential adopts the Higgs potential form with a mildlytime-evolving vacuum expectation value. Such residual vacuum dynamics could beresponsible for the possible time variation of the fundamental constants. Theapproach is in part reminiscent of Bjorken's ideas on the cosmological constantproblem.

Higgs potential from extended Brans-Dicke theory and the time-evolution of the fundamental constants