Effective Equations of Cosmological Models in (loop) Quantum Gravity

Open Access
Author:
Simpson, David Bryant
Graduate Program:
Physics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 07, 2013
Committee Members:
  • Martin Bojowald, Committee Chair
  • Jainendra Jain, Committee Member
  • Richard Wallace Robinett, Committee Member
  • Ping Xu, Committee Member
Keywords:
  • quantum cosmology
  • effective equations
  • Hamiltonian constraint
  • factor ordering
  • electric time
  • non-linear discrete Schrödinger
Abstract:
This dissertation focuses on the properties of several differing models within quantum cosmology. Specifically, by using the method of effective equations, we explore: a linear discrete Schrödinger model, a non-linear discrete Schrödinger model, factor ordering ambiguities in the Hamiltonian constraint (with a focus on large-volume behavior), and the use of the electric vector potential as deparameterized time. In the linear and non-linear Schrödinger models, we arrive at a new possibility for studying inhomogeneous quantum cosmology (where the non-linearities are interpreted as non-local deviations from the spatial average) that allows for a variety of dynamics and raises a number of questions for future research. We then turn our focus to the general effects of factor ordering ambiguities and their possible role in large-volume collapse of a k = 0 isotropic quantum cosmology with a free, massless scalar field. With the additional inclusion of holonomy and inverse-triad corrections, the choice in factor ordering of the Hamiltonian constraint is quite relevant; however, with our assumptions, we do not see any significant departure from classical large-volume behavior. The final model discussed is formulated with the electric vector potential as the global internal time in a Wheeler–DeWitt setting sourced by radiation. While further analysis is required to make a definitive statement on the impact that the choice of deparameterization makes, we find that the specific form of quantum state can affect early-universe dynamics and even lead to new possibilities.