A SCALAR-TENSOR THEORY OF GRAVITY BASED ON NONCOMMUTATIVE GEOMETRY

The unified description of gauge and Higgs fields based on non-commuta tive geometry due to Connes has a similar structure to Kaluza-Klein th eory, though it is a 4-dimensional theory. Its extension to a theory i n curved spacetime is, then, expected to give a Brans-Dicke type gravi ty in which Higgs-like scalar fields couple to the gravitational field . In this paper, we study a B-D type gravity using the matrix coordina te method originated by Coquereaux. In particular, the introduction of two kinds of scalar fields is discussed in detail from the viewpoint of cosmology.