Deformed General Relativity and Effective actions in Quantum Gravity
Open Access
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 31, 2013
- Committee Members:
- Martin Bojowald, Dissertation Advisor
- Abhay Vasant Ashtekar, Committee Member
- John Collins, Committee Member
- Ping Xu, Committee Member
- Keywords:
- Quantum Gravity
- Deformed algebras
- Modified Gravity
- General Relativity
- Signature change
- Effective actions
- Abstract:
- We will use canonical methods to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, we extend classical constructions systematically to effective constraints of canonical quantum gravity and apply these constructions to model systems as well as general metrics, with the following conclusions: (i) Dispersion relations of matter and gravitational waves are deformed in related ways, ensuring a consistent realization of causality. (ii) Inverse-triad corrections modify the classical action in a way clearly distinguishable from curvature effects. In particular, these corrections can be signi cantly larger than often expected for standard quantum-gravity phenomena. (iii) Finally, holonomy corrections in high-curvature regimes do not signal the evolution from collapse to expansion in a "bounce," but rather the emergence of the universe from Euclidean space at high density. This new version of signature-change cosmology suggests a natural way of posing initial conditions, and a solution to the entropy problem. The aforementioned corrections of canonical quantum gravity modify spacetime structures, sometimes to the degree that no effective line elements exist to describe the geometry. An analysis of solutions, for instance in the context of black holes, then requires new insights. In this dissertation, standard definitions of horizons in spherical symmetry are first reformulated canonically, and then evaluated for solutions of equations and constraints modi ed by inverse-triad corrections of loop quantum gravity. For more general conclusions, canonical perturbation theory is developed to second order to include back-reaction from matter. The work described in this dissertation regarding deformed algebras and their implications for space-time, matter, the universe, and black holes is based on previous publications by the author and his collaborators, which may be consulted for further details and references.