The cosmological probability density function for Bianchi class A models in quantum supergravity.

Nicolai's theorem suggests a simple stochastic interpetation for supersymmetric Eu-clidean quantum theories, without requiring any inner product to be defined on the space of states. In order to apply this idea to supergravity, we first reduce to a one-dimensional theory with local supersymmetry by the imposition of homogeneity conditions. We then make the supersymmetry rigid by imposing gauge conditions, and quantise to obtain the evolution equation for a time-dependent wave function. Owing to the inclusion of a certain boundary term in the classical action, and a careful treatment of the initial conditions, the evolution equation has the form of a Fokker-Planck equation. Of particular interest is the static solution, as this satisfies all the standard quantum constraints. This is naturally interpreted as a cosmolog-ical probability density function, and is found to coincide with the square of the magnitude of the conventional wave function for the wormhole state.