Cosmological time in quantum supergravity

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