On gravity's role in the genesis of rest masses of classical fields

TL;DR

This paper explores how gravitational effects influence the stability of vacuum states and the generation of rest masses in classical fields within an Einstein-Higgs-Maxwell framework, identifying a critical curvature for mass genesis.

Contribution

It demonstrates the existence of a critical mean curvature in cosmological models where rest masses can form, linking gravity to mass generation mechanisms.

Findings

Stable vacuum states exist only below a critical curvature.

Mass generation via Higgs mechanism depends on gravitational conditions.

Extreme gravity can prevent the definition of rest masses.

Abstract

It is shown that in the Einstein-conformally coupled Higgs--Maxwell system with Friedman-Robertson-Walker symmetries the energy density of the Higgs field has stable local minimum only if the mean curvature of the $t={\rm const}$ hypersurfaces is less than a finite critical value $\chi_c$, while for greater mean curvature the energy density is not bounded from below. Therefore, there are extreme gravitational situations in which even quasi-locally defined instantaneous vacuum states of the Higgs sector cannot exist, and hence one cannot at all define the rest mass of all the classical fields. On hypersurfaces with mean curvature less than $\chi_c$ the energy density has the `wine bottle' (rather than the familiar `Mexican hat') shape, and the gauge field can get rest mass via the Brout--Englert--Higgs mechanism. The spacelike hypersurface with the critical mean curvature represents the moment of `genesis' of rest masses.