General Relativity & Quantum Cosmology

The parametrized particle: notion of Dirac observables - Canonical analysis of the first order action for 3D gravity - Constraints of 3D gravity (1st order formulation): Gauss constraints and Flatness constraints.

Hamiltonian formulation of constrained systems: examples from tutorial 1; notions of primary, secondary... constraints and notions of first class and second class constraints - Relation constraints/gauge symmetries - A totally constrained system: the parametrized particle.

The characteristics of black holes smaller than the Planck scale are addressed.  These result from a modified metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution has two interesting features: first, it naturally implies the Generalized Uncertainty Principle. Secondly, this metric exhibits an effective dimensional reduction feature, indicating that the gravitational physics of the sub-Planckian regime is effectively (1+1)-D.

In this talk, I will discuss the asymptotic safety paradigm, and will highlight that it can provide a framework for a predictive ultraviolet completion for gravity and matter. Specifically, I will discuss compelling hints that exist for the realization of asymptotic safety in pure gravity, and will then present recent progress on the case of gravity coupled to Standard Model matter. In particular, I will highlight results that show how to forge a link between physics at the Planck scale and physics at the electroweak scale, in order to impose observational constraints on the microscopic quantum gravity dynamics.