The Higgs Field and the Jordan Brans Dicke Cosmology

TL;DR

This paper explores a cosmological model linking the Higgs field with the Jordan-Brans-Dicke theory, revealing how particle masses and universe expansion relate through a coupled scalar field framework.

Contribution

It introduces a novel interpretation of JBD theory with a Higgs-like potential, deriving a coupled scalar field model with spontaneous symmetry breaking in a cosmological context.

Findings

Derived a coupled scalar field Lagrangian with Higgs mechanism in cosmology.

Identified a vacuum expectation value for the Higgs field in an expanding universe.

Demonstrated spontaneous symmetry breaking in the cosmological scalar field model.

Abstract

We investigate a field theoretical approach to the Jordan-Brans- Dicke (JBD) theory extended with a particular potential term on a cosmological background by starting with the motivation that the Higgs field and the scale factor of the universe are related. Based on this relation, it is possible to come up with mathematically equivalent but two different interpretations. From one point of view while the universe is static, the masses of the elementary particles change with time. The other one, which we stick with throughout the manuscript, is that while the universe is expanding, particle masses are constant. Thus, a coupled Lagrangian density of the JBD field and the scale factor (the Higgs field), which exhibit a massive particle and a linearly expanding space in zeroth order respectively, is obtained. By performing a coordinate transformation in the field space for the reduced JBD action whose kinetic part is nonlinear sigma model, the Lagrangian of two scalar fields can be written as uncoupled for the Higgs mechanism. After this transformation, as a result of spontaneous symmetry breaking, the time dependent vacuum expectation value (vev) of the Higgs field and the Higgs bosons which are the particles corresponding to quantized oscillation modes about the vacuum, are found.