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

TL;DR

This paper links the Higgs potential to an extended Brans-Dicke gravity theory with two scalar fields, suggesting a dynamic vacuum that could explain the possible time variation of fundamental constants.

Contribution

It introduces a gravity-based origin for the Higgs potential using an extended Brans-Dicke model with two interacting scalar fields, leading to a time-evolving vacuum expectation value.

Findings

The effective scalar potential resembles the Higgs potential.

The vacuum expectation value evolves mildly over time.

Residual vacuum dynamics may cause variations in fundamental constants.

Abstract

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.