Scalar field vacuum expectation value induced by gravitational wave background

Patrick McDougall,Preston Jones,Douglas Singleton,Michael Ragsdale

doi:10.1016/j.physletb.2018.04.055

Patrick McDougall, Preston Jones + Show 2 more

Open Access

https://doi.org/10.1016/j.physletb.2018.04.055

Copy DOI

Abstract

We show that a massless scalar field in a gravitational wave background can develop a non-zero vacuum expectation value. We draw comparisons to the generation of a non-zero vacuum expectation value for a scalar field in the Higgs mechanism and with the dynamical Casimir vacuum. We propose that this vacuum expectation value, generated by a gravitational wave, can be connected with particle production from gravitational waves and may have consequences for the early Universe where scalar fields are thought to play an important role.

Highlights

The Brout–Englert–Higgs mechanism [1] is one of the cornerstones of the Standard Model of particle physics
We have shown that a massless scalar field placed in a plane, gravitational wave background will develop a space–time dependent, non-zero vacuum value given by (14) (15) even in the limit when all the momentum parameters of the scalar field are taken to zero
This is different from what happens to the massless scalar field solution in Minkowski space–time, where when one takes the zero energy-momentum limit the scalar field vanishes

Summary

Introduction

The Brout–Englert–Higgs mechanism [1] is one of the cornerstones of the Standard Model of particle physics. The arbitrary choice of θ = 0 as the vacuum for This non-zero vacuum expectation value of the scalar field is responsible for giving masses to the W ± and Z 0 gauge bosons of the SU (2) × U (1) Standard Model, while leaving the photon massless. In the Ginzburg–Landau model the source of the non-zero order parameter/scalar field vacuum expectation value is due to the interaction between the electrons and the phonons of the background lattice. We make a comparison of this gravitationally induced effect with the scalar field vacuum expectation value of spontaneous symmetry breaking as found in the Higgs mechanism and the Ginzburg–Landau model. There is very recent work [11] which discusses the consequences of the interaction of a gravitational wave background with a time-dependent vacuum expectation value from a (nonAbelian) gauge field

Approximate gravitational wave background

Exact gravitational wave background

Discussion and conclusions