De Sitter spaces: topological ramifications of gravity as a gauge theory

Abstract

We exploit an interpretation of gravity as the symmetry-broken phase of a de Sitter gauge theory to construct new solutions to the first-order field equations. The new solutions are constructed by performing large Spin(4, 1) gauge transformations on the ordinary de Sitter solution and extracting first the tetrad, and then the induced metric. The class of metrics so obtained is an infinite class labeled by an integer, q. Each solution satisfies the local field equations defining constant positive curvature and is therefore locally isometric to de Sitter space wherever the metric is non-degenerate. The degeneracy structure of the tetrad and metric reflects the topological differences among the solutions with different q. By topological arguments we show that the solutions are physically distinct with respect to the symmetries of Einstein–Cartan theory. Ultimately, the existence of solutions of this type may be a distinguishing characteristic of gravity as a metric theory versus gravity as a gauge theory.