The Case for a Gravitational de Sitter Gauge Theory

Abstract

With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincar\'e group as the obvious choice. This theory gives Einstein's equations in a particular case, and Newton's law in the static non-relativistic limit, being seemingly sound at the classical level. But it comes out that it is not quantizable. The usual procedure of adding counterterms to make it a consistent and renormalizable theory leads to two possible theories, one for each of the two de Sitter groups, SO(4,1) and SO(3,2). The consequences of changing from the Poincar\'e to the de Sitter group, as well as the positive aspects, perspectives and drawbacks of the resulting theory are discussed.