# The Cosmological Probability Density Function for Bianchi Class A Models in Quantum Supergravity

## Authors

**Hugh Luckock** and **Chris Oliwa**

## Status

Research Report 94-42

Date: 9 December 1994

## Abstract

Nicolai's theorem suggests a simple stochastic interpretation for
supersymmetric Euclidean 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
cosmological probability density function, and is found to coincide with the
square of the magnitude of the conventional wave function for the wormhole
state.

## Key phrases

canonically quantised supergravity. homogeneous cosmologies.
interpretation of the wave function.

## AMS Subject Classification (1991)

Primary: 83E50

Secondary: 83F05, 83C45, 83C20, 81Q60
## Content

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