Loop Quantum Cosmology: Anisotropies and Inhomogeneities

Open Access
Wilson-Ewing, Edward
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
December 02, 2010
Committee Members:
  • Abhay Vasant Ashtekar, Dissertation Advisor
  • Abhay Vasant Ashtekar, Committee Chair
  • Martin Bojowald, Committee Member
  • Nigel David Higson, Committee Member
  • Paul Sommers, Committee Member
  • loop quantum gravity
  • cosmology
In this dissertation we extend the improved dynamics of loop quantum cosmology from the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-times to cosmological models which allow anisotropies and inhomogeneities. Specifically, we consider the cases of the homogeneous but anisotropic Bianchi type I, II and IX models with a massless scalar field as well as the vacuum, inhomogeneous, linearly polarized Gowdy T3 model. For each case, we derive the Hamiltonian constraint operator and study its properties. In particular, we show how in all of these models the classical big bang and big crunch singularities are resolved due to quantum gravity effects. Since the Bianchi models play a key role in the Belinskii, Khalatnikov and Lifshitz conjecture regarding the nature of generic space-like singularities in general relativity, the quantum dynamics of the Bianchi cosmologies are likely to provide considerable intuition about the fate of such singularities in quantum gravity. In addition, the results obtained here provide an important step toward the full loop quantization of cosmological space-times that allow generic inhomogeneities; this would provide falsifiable predictions that could be compared to observations.