Mach's Principle and Model for a Broken Symmetric Theory of Gravity

TL;DR

This paper explores a conformally invariant gravitational model where spontaneous symmetry breaking leads to variable inertial masses and a mechanism for relaxing vacuum energy, aligning with Mach's principle in a cosmological setting.

Contribution

It introduces a scalar tensor theory with spontaneous symmetry breaking that connects gravitational coupling to Mach's principle and provides a mechanism for vacuum energy relaxation.

Findings

Inertial masses vary with cosmological conditions.

The model supports Mach's principle in a dynamic universe.

Vacuum energy density relaxes over cosmic evolution.

Abstract

We investigate spontaneous symmetry breaking in a conformally invariant gravitational model. In particular, we use a conformally invariant scalar tensor theory as the vacuum sector of a gravitational model to examine the idea that gravitational coupling may be the result of a spontaneous symmetry breaking. In this model matter is taken to be coupled with a metric which is different but conformally related to the metric appearing explicitly in the vacuum sector. We show that after the spontaneous symmetry breaking the resulting theory is consistent with Mach's principle in the sense that inertial masses of particles have variable configurations in a cosmological context. Moreover, our analysis allows to construct a mechanism in which the resulting large vacuum energy density relaxes during evolution of the universe.