%0 Journal Article
%T Discrete Symmetry, Non-Commutative Geometry and Gravity
%A N. Mohammedi
%J Physics
%D 1992
%I arXiv
%X We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the vierbeins are extended to incorporate additional scalar and vector fields. The resulting action describes two universes coupled in a non-minimal way to a set of scalar fields. This picture is slightly different from the description of general relativity in the framework of non-commutative geomety.
%U http://arxiv.org/abs/gr-qc/9211015v1