PHYSICAL STATES OF BIANCHI TYPE-IX QUANTUM COSMOLOGIES DESCRIBED BY THE CHERN-SIMONS FUNCTIONAL

A class of exact solutions of the Wheeler-De-Witt equation for diagona l Bianchi type IX cosmologies with a cosmological constant is derived in the metric representation. This class consists of all the ''topolog ical solutions'' which are associated with the Bianchi type IX reducti on of the Chern-Simons functional in Ashtekar variables. The different solutions within the class arise from the topologically inequivalent choices of the integration contours in the transformation from the Ash tekar representation to the metric representation. We show how the sad dle points of the reduced Chern-Simons functional generate a complete basis of such integration contours and the associated solutions. Among the solutions we identify. two, which, semiclassically, satisfy the b oundary conditions proposed by Vilenkin and by Hartle and Hawking, res pectively. In the limit of a vanishing cosmological constant our solut ions reduce to a class found earlier in special fermion sectors of sup ersymmetric Bianchi type IX models.