DISCRETE SYMMETRY, NONCOMMUTATIVE GEOMETRY AND GRAVITY

We consider gravity using the formalism of a differential Z2-graded algebra of 2 x 2 matrices whose elements are differential forms on space-time. The connection and the orthonormal frame are extended to incorporate additional scalar and vector fields. The extended torsion-free constraints are solved for a simple case. The resulting action describes a set of scalar fields minimally coupled to Einstein-Hilbert gravity.