Higgs mechanism for gravity

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 noninflaton 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.

Figure 1

The potential $V({\phi }_{ij},\varphi )$. The metric is conformally flat for $\varphi >{\varphi }_c$, tachyonic for $\varphi <{\varphi }_c$, and becomes massless at the minimum of the potential at $\varphi =0$, $|{\phi }_{ij}|=\pm M$.

Figure 2

The breaking of translational invariance.