Cosmological Time in Quantum Supergravity

TL;DR

This paper explores the canonical quantization of a supergravity theory where the cosmological constant is dynamical, leading to a natural notion of time and a conserved probability density, addressing the problem of time in quantum gravity.

Contribution

It introduces a formulation of supergravity with a dynamical cosmological constant that allows for a well-defined time evolution in quantum theory.

Findings

Wave function evolves with a dynamical variable as time

Probability density obeys conservation equations

Avoids traditional time problems in quantum gravity

Abstract

The version of supergravity formulated by Ogievetsky and Sokatchev is almost identical to the conventional $N=1$ 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 quantisation 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.