Supersymmetric Homogeneous Quantum Cosmologies Coupled to a Scalar Field

Abstract

Recent work on $N=2$ supersymmetric Bianchi type IX cosmologies coupled to a scalar field is extended to a general treatment of homogeneous quantum cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX, describing a virtual wormhole fluctuation, an additional explicit solution is given and identified with the `no-boundary state'.