Monte Carlo simulation of cosmologies with dust

The quantum theory of the Friedmann cosmological model with dust and cosmological constant () is not exactly solvable analytically. We apply path integral Monte Carlo (PIMC) techniques to study its quantum dynamics using the physical Hamiltonian corresponding to the dust field as a clock. We study (i) quantum fluctuations around classical paths and (ii) formulate the analogues of the no-boundary and tunnelling proposals and simulate the ground state wave functions. For a unique ground state wave function exists. For the physical Hamiltonian is not bounded below, but the path integral for the propagator is convergent over a range of Euclidean time T. We investigate the properties of the convergent propagator. The path integral can be made convergent for all values of T by restricting the integral over paths with action greater than equal to zero. We explore the consequences of such a choice.