COSMOLOGICAL TIME IN QUANTUM SUPERGRAVITY

The version of supergravity formulated by Ogievetsky and Sokatchev is almost identical to the conventional N=1 theory, except that the cosmo logical constant Lambda appears as a dynamical variable which is const ant only by virtue of the field equations. We consider the canonical q uantization of this theory, and show that the wave function evolves wi th respect to a dynamical variable which can be interpreted as a cosmo logical time parameter. The square of the modulus of the wave function obeys a set of simple conservation equations and can be interpreted a s a probability density functional. The usual problems associated with time in quantum gravity are avoided.