Monte Carlo quantum cosmology with a modified Euclidean action

Abstract

We numerically study the Euclidean quantum cosmology of a closed, homogeneous and isotropic universe with a cosmological constant. A dust field acts as a clock, and we compute the ground state wavefunction, correlation function, and mean volume of the universe by performing path integral Monte Carlo simulations. To make the path integral convergent, the argument of the exponent in the weight of the path integral is chosen to be either the absolute value of the Euclidean action, or its square. We compare our results to the standard case (with a hard cutoff at zero action), and find that the absolute value produces similar results, whereas the squared method gives substantially different results. We detail two different methods of `fixing' the squared case, and test them for the simple harmonic oscillator, and for this cosmological model. We also find that for a large positive cosmological constant, the universe undergoes multiple cycles of expansion and contraction for all three weights, and reaches much larger sizes with the squared weight.