A Higgs Mechanism for Gravity

TL;DR

This work presents a framework in which spacetime and gravity arise from a sequence of rapid symmetry breakings of the diffeomorphism group. By employing nonlinear realizations of $Diff(n,\mathbb{R})$ over successive stabilizers, it treats coordinates, the affine connection, and the metric as Goldstone fields, unifying gravitational degrees of freedom through coset dynamics. A Higgs mechanism is then proposed where the metric condenses in an affine spacetime, breaking $GL(n,\mathbb{R})$ to $SO(1,n-1)$ and driving the system toward a Riemannian geometry; the metric is absorbed into the connection, nonmetricity becomes Planck-suppressed, and General Relativity emerges as a low-energy effective theory. The model draws a hybrid-inflation-like potential for the symmetry-breaking sector and discusses a dynamical fluid of reference from Goldstone coordinates, linking cosmological evolution to fundamental symmetry principles. If borne out, this emergent-spacetime picture offers a group-theoretic origin for gravity and a novel route to link early-universe dynamics with late-time GR phenomenology.

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.

Figures (2)

• Figure 1: The potential $V(\varphi_{ij}, \phi)$. The metric is conformally flat for $\phi> \phi_c$, tachyonic for $\phi<\phi_c$ and becomes massless at the minimum of the potential at $\phi=0$, $\vert \varphi_{ij} \vert = \pm M$.
• Figure 2: The breaking of translational invariance.