Loop Quantum Cosmology and the Early Universe

Open Access
Sloan, David
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
June 01, 2010
Committee Members:
  • Abhay Vasant Ashtekar, Dissertation Advisor
  • Abhay Vasant Ashtekar, Committee Chair
  • Martin Bojowald, Committee Member
  • Tyce De Young, Committee Member
  • Nigel David Higson, Committee Member
  • Loop Quantum Cosmology
  • Loop Quantum Gravity
  • Inflation
  • Measures of Probability
In this dissertation we explore two issues relating to Loop Quantum Cosmology (LQC) and the early universe. The first is expressing the Belinkskii, Khalatnikov and Lifshitz (BKL) conjecture in a manner suitable for loop quantization. The BKL conjecture says that on approach to space-like singularities in general relativity, ‘time derivatives dominate over spatial derivatives’ so that the dynamics at any spatial point is well captured by a set of coupled ordinary differential equations. A large body of numerical and analytical evidence has accumulated in favor of these ideas, mostly using a framework adapted to the partial differential equations that result from analyzing Einstein's equations. By contrast we begin with a Hamiltonian framework so that we can provide a formulation of this conjecture in terms of variables that are tailored to non-perturbative quantization. We explore this system in some detail, establishing the role of `Mixmaster' dynamics and the nature of the resulting singularity. Our formulation serves as a first step in the analysis of the fate of generic space-like singularities in loop quantum gravity. The second issue is that of the role of inflation in LQC. In LQC the big bang singularity is replaced by a quantum bounce which is followed by a robust phase of super-inflation. We establish the behavior of effective equations for LQC in a generic setting then investigate in detail the particular case of early universe inflation caused by the slow roll of a scalar field down its potential. A natural measure is formed on the space of solutions to the equations of motion and it is established that in this scenario the a priori probability of seeing the required 68 efolds of inflation is in fact very high which stands in stark contrast to the results that have been presented in the classical case. In doing so we show that inflation in LQC suffers from no `fine tuning' issue and is in fact a generic feature.