LOOP GRAVITY: AN APPLICATION AND AN EXTENSION

Open Access
Author:
Taveras, Victor Manuel
Graduate Program:
Physics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 19, 2009
Committee Members:
  • Abhay Vasant Ashtekar, Dissertation Advisor
  • Abhay Vasant Ashtekar, Committee Chair
  • Martin Bojowald, Committee Member
  • Lee S Finn, Committee Member
  • Nigel David Higson, Committee Member
Keywords:
  • Holst action
  • loop quantum cosmology
  • cosmology
Abstract:
In this thesis we address two issues in the area of loop quantum gravity. The first concerns the semiclassical limit in loop quantum cosmology via the use of so-called effective equations. In loop quantum cosmology the quantum dynamics is well understood. We can approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen semiclassical states. This submanifold is isomorphic with the classical phase space and the projected dynamical flow provides effective equations incorporating the leading quantum corrections to the classical equations of motion. Numerical work has been done in the full theory using quantum states which are semiclassical at late times. These states follow the classical trajectory until the density is on the order of 1\% of the Planck density then deviate strongly from the classical trajectory. The effective equations we obtain reproduce this behavior to surprising accuracy. The second issue concerns generalizations of the classical action which is the starting point for loop quantum gravity. In loop quantum gravity one begins with the Einstein-Hilbert action, modified by the addition of the so-called Holst term. Classically, this term does not affect the equations of motion, but it leads to a well-known quantization ambiguity in the quantum theory parametrized by the Barbero--Immirzi parameter, which rescales the eigenvalues of the area and volume operators. We consider the theory obtained by promoting the Barbero--Immirzi parameter to a field. The resulting theory, called Modified Holst Gravity,is equivalent to General Relativity coupled to a pseudo-scalar field. However, this theory turns out to have an unconventional kinetic term for the Barbero-Immirzi field and a rather unnatural coupling with fermions. We then propose a further generalization of the Holst action, which we call Modified Nieh--Yan Gravity, which yields a theory of gravity and matter with a more natural coupling to the Barbero--Immirzi field. We conclude by commenting on possible implications for cosmology, induced by the existence of this new pseudo-scalar field.