General Relativity & Quantum Cosmology

Theories of gravity having connection as an independent dynamical variable can have a massive spin -2 particle together with the massless graviton in their spectrum. We study the potentiality of such models as a consistent infrared modification of gravity. It will be shown that these models are free from ghost like Boulware-Deser mode in the background of arbitrary torsionless Einstein manifolds. At least for weak for weak enough curvature the dangerous spin zero mode has a healthy kinetic energy in our backgrounds. vDVZ singularity seems to be a generic feature which may be cured by Vainshtein mechanism as in other infrared modified theories of gravity.

We consider a codimension-2 brane inflation scenario in a warped flux compactification of 6D gauged supergravity. The volume modulus of the model is stabilized by means of potentials localized on the regularized background branes. We discuss the cosmological evolution of the world-volume of a probe codimension-2 brane when it moves along the radial direction of the internal space. In order to have slow-roll inflation, we find that the warping of the internal space is required to be weak, in contrast to the string inflation constructions with strong warping. We discuss the parameter range that the inflation is in agreement with the observationally inferred parameters and which furthermore is consistent with the probe brane approximation. We argue that from a multi-brane solution, the backreaction of the probe brane on the weak warp factor is ignorable

Models with two supersymmetric large extra dimensions (SLED) may provide a way to approach both the cosmological constant problem and dark energy. After reviewing these ideas, I shall discuss warped brane world solutions in 6D supergravity, as a laboratory in which to explore SLED and codimension two branes in general. Solving the linearized perturbations for all the bosonic fields, and some of the fermions, we can observe how the corresponding physics compares with 5D models and standard Kaluza-Klein compactifications. These results should help to better our understanding of the cancellations in the 4D effective vacuum energy with SLED.

In my talk I will provide an overview of the applications of Wilson's modern renormalization group (RG) to problems in quantum gravity. I will first discuss the development of the RG for continuum gravity within the framework of Feynman's covariant path integral approach. Then I will discuss a number of issues that arise when implementing the path integral approach with an explicit lattice UV regulator, and later how non-perturbative RG flows and universal non-trivial scaling dimensions can in principle be extracted from these calculations. Towards the end I will discuss recent attempts at formulating RG flows for gravitational couplings within the framework of a set of manifestly covariant, but non-local, effective field equations suitable for quantum cosmology.

Philosophy of physics, puzzles about the content and status of foundational principles – the logic of physicists’ basic assumptions, especially with regards to space and time, and the history of science, e.g. exactly how Einstein made his discoveries.

Quantum gravity, quantum processes in the early universe, evaporation of black holes, limits on the measurements made by real detectors (coupled to the environment), and with regards to mathematical problems, studying techniques rather than finding solutions.