Quantum Aspects of Cosmology

Abstract

It is an interesting task to view the entire universe using quantum mechanics. (Here by the entire universe I mean both the space-time and matter.) And the question of how to do so has been pondered upon by a few minds including those of Wheeler, DeWitt, James Hartle, Stephen Hawking etc. As answers to many questions two formalism viz, the path integral formalism and the canonical formalism were introduced and used to understand the quantum aspects of the universe (or Quantum Gravidynamics). These allow one to construct, for very simple model universes, their wavefunctionals and consequently calculate the expectation values of required observables. In the following sections we will start by familiarizing ourselves with the concept of wavefunctionals with a couple of simple model examples from QFT. Following this, we look at the Path integral formalism developed for quantum gravidynamics and summarize a paper which points out an inconsistency in two age old proposals. I will keep the canonical formalism for later, as it becomes a crucial part of the second half of the project. Here, I will briefly introduce a few problems faced in the canonical quantization. Thereafter we will understand Geometric Quantization as it gives a natural Hilbert space construction for the respective classical systems. This will allow us to understand better the Hilbert space problem in the canonical theory. As work is still in progress, I conclude this thesis by remarking on how Geometric Quantization comes to the rescue.