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

Nicolai's theorem suggests a simple stochastic interpetation 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.Comment: 22 pages, Late

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 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.Comment: 12 pages, LaTe

The Effect of Higher-Order Curvature Terms on String Quantum Cosmology

Several new results regarding the quantum cosmology of the quadratic gravity theory derived from the heterotic string effective action are presented. After describing techniques for solving the Wheeler-De Witt equation with appropriate boundary conditions, it is shown that this quantum cosmological model may be compared with semiclassical theories of inflationary cosmology. In particular, it should be possible to compute corrections to the standard inflationary model perturbatively about a stable exponentially expanding classical background.Comment: 24 pages, TeX. Several remarks on operator ordering, the complete computation of $H_1\psi_0$, and approximate solutions of the $a$ and $\Phi$ equations of motion, which are stable and exponentially expanding, have been included. Substantial revision of equations (5)-(7), (10)-(20) from version