Application of Monte Carlo simulation methods to quantum cosmology.

Abstract

Quantum Monte Carlo (MC) simulation methods used widely throughout physics to generate ground-state wave functions are applied to the minisuperspace quantization of spatially homogeneous cosmologies. MC diffusion, MC path integral, and semiclassical MC path integral methods are applied to the de Sitter model, the mixmaster universe (and its generalizations), and the Robertson-Walker scalar field cosmology. All methods adequately reproduce the de Sitter model's wave function in the regime that has an effective ground state. In other situations, the failure of the Hamiltonian constraint (i.e., Wheeler-DeWitt operator) to be bounded from below presents a severe obstacle to the simulations. If a ground state is artificially forced, the various MC methods can be compared in more complicated models. The simulations can then be used to study issues such as the validity of the minisuperspace approximation, the choice of a time variable, the path space measure, and tunneling universe wave functions.