A Higgs Mechanism for Gravity

TL;DR

This paper proposes a Higgs mechanism for gravity where spacetime structures emerge from symmetry breaking, with the metric acting as a Higgs field, leading to a transition from affine to Riemannian geometry.

Contribution

It introduces a novel Higgs mechanism for gravity using nonlinear realizations of diffeomorphisms, interpreting gravitational fields as Goldstone bosons, and models spacetime emergence via metric condensation.

Findings

Gravitational fields can be viewed as Goldstone fields of diffeomorphism symmetry.

A Higgs mechanism for gravity is constructed with a metric tensor as a Higgs field.

Spacetime transitions from affine to Riemannian through metric condensation.

Abstract

In this paper we elaborate on the idea of an emergent spacetime which arises due to the dynamical breaking of diffeomorphism invariance in the early universe. In preparation for an explicit symmetry breaking scenario, we consider nonlinear realizations of the group of analytical diffeomorphisms which provide a unified description of spacetime structures. We find that gravitational fields, such as the affine connection, metric and coordinates, can all be interpreted as Goldstone fields of the diffeomorphism group. We then construct a Higgs mechanism for gravity in which an affine spacetime evolves into a Riemannian one by the condensation of a metric. The symmetry breaking potential is identical to that of hybrid inflation but with the non-inflaton scalar extended to a symmetric second rank tensor. This tensor is required for the realization of the metric as a Higgs field. We finally comment on the role of Goldstone coordinates as a dynamical fluid of reference.