  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.
