de Sitter Spaces

Understand

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, then the induced metric.
• The class of metrics so obtained is an infinite class labelled 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.