Some implications of gravity with de Sitter tangent space

Abstract

Einstein theory of gravity could be formulated as a gauge theory with the tangent space representing either Lorentz symmetry or de Sitter symmetry. In curved space-time this symmetry is realized as a local symmetry of the tangent manifold. In presence of space-time spinors this symmetry becomes relevant as these couple to the spin-connection which is identified with the gauge fields. In the absence of matter interactions, both formulations are equivalent to Einstein’s gravity expressed in terms of the space-time metric. The equivalence seizes when coupled to matter which will have different representations with respect to the tangent space group. The purpose of the first part of this thesis is to investigate the coupling of gravity to matter when the tangent space group is the de Sitter group and to find modifications to the action in the case of spinors and vectors. In particular it will be interesting to look for spherically symmetric solutions for the equations of motion. The situation in three space-time dimensions is more involved. The gravi-tational Chern-Simons theory with the gauge groups SO(1; 3) is known to be equivalent to Einstein’s theory with cosmological constant. This Chern-Simons theory is different than the gravitational action constructed with the gauge group SO(1; 3). In particular the Chern-Simons theory does not allow the coupling to matter, while the new formulation allows for matter interaction. The aim of the second part of this thesis is to study the difference between topological gravity and the new formulation of three dimensional gravity.