Date of Degree
V. Parameswaran Nair
In the search for a theory of Quantum Gravity a new proposal was recently made by P. Hořava. The main feature of this new proposed theory is that it is power-counting renormalizable by construction, and could prove to be truly renormalizable, although more work is needed in this direction.
The renormalizability of the theory is a central issue. Indeed, General Relativity does not have this property, implying that to construct its quantum version we need to “complete” the theory in the UV. Hořava suggested a possible way to provide a UV completion of GR by giving up full spacetime reparametrization symmetry, which is one of the fundamental assumptions of GR, and adding appropriate higher order terms in the action.
In this Thesis we review Hořava’s theory and analyze some of the issues related to the breaking of the spacetime structure.
Specifically, we derive the general static spherically symmetric solutions for Hořava’s theory with a nonvanishing radial “shift” field gtr. Such “hedgehog” configurations are not considered in GR, since gtr can be mapped to zero with an appropriate reparametrization, but they are physically distinct solutions in Hořava gravity where the reparametrization is not allowed by the reduced symmetry. These new solutions exhibit specific properties from the particle dynamics point of view and possess an extra gauge symmetry.
We also study the deformed kinematics of point particles allowed by the reduced reparametrization symmetry. The main result is that particles can have generalized dispersion relations that include higher even powers of the momentum. We analyze the implications of this and provide some examples that may be converted into possible experimental tests for the deviations of this new theory of gravity from standard GR.
Capasso, Dario, "Hořava Gravity: Symmetries and Generalized Particle Dynamics" (2011). CUNY Academic Works.