  Despite the enormous significance of the Higgs potential in the context of
the Standard Model of electroweak interactions and in Grand Unified Theories,
its ultimate origin is fundamentally unknown and must be introduced by hand in
accordance with the underlying gauge symmetry and the requirement of
renormalizability. Here we propose a more physical motivation for the structure
of the Higgs potential, which we link to gravity, and more specifically to an
extended Brans-Dicke (BD) theory containing two interacting scalar fields. One
of these fields is coupled to curvature as in the BD formulation, whereas the
other is coupled to gravity both derivatively and non-derivatively through the
curvature scalar and the Ricci tensor. By requiring that the cosmological
solutions of the model are consistent with observations, we show that the
effective scalar field potential adopts the Higgs potential form with a mildly
time-evolving vacuum expectation value. Such residual vacuum dynamics could be
responsible for the possible time variation of the fundamental constants. The
approach is in part reminiscent of Bjorken's ideas on the cosmological constant
problem.
