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/Co-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.