Bouncing Universes: Simple Cosmological Models with a Scalar Field

Abstract

In this thesis, we consider a homogeneous and isotropic closed model of the Universe with a real massive scalar field. Hawking showed that if such a model of the Universe is fine-tuned, it can have an infinite number of bounces. We study the case for the Universe that is microscopically time-symmetric about a homogeneous, isotropic bounce. We begin by considering a classical periodic solution in which a Universe has a time-symmetric bounce and expands to a large maximum size with a fixed large number of zero crossings of the scalar field between each pair of consecutive bounces. After the inflation, the scalar field oscillates with a phase constant. The change in this oscillation phase will quantify a perturbation of the solution and we are seeking to find the probability for two successive bounces.