Quantum Gravity

We show that the matrix-model for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. The nonabelian gauge fields as well as additional scalar fields couple to a dynamical metric G_ab, which is given in terms of a Poisson structure. This leads to a gravity theory which is naturally related to noncommutativity, encoding those degrees of freedom which are usually interpreted as U(1) gauge fields. Essential features such as gravitational waves and the Newtonian limit are reproduced correctly. UV/IR mixing is understood in terms of an induced gravity action. The framework appears suitable for quantizing gravity.

After a brief motivation for studying 3d gravity, a review of Strominger argument will be given, showing that 3d quantum gravity with negative cosmological constant is a conformal field theory. Classical phase space tools will be introduced to develop semi-classical analyses of gravity with zero cosmological constant, and, with negative cosmological constant and closed timelike curves.

There has been much interest, in the past few years, in the kappa-Poincare\'/kappa-Minkowski framework as a possible scenario for a deformation of Poincare\' symmetries at Planck scale. I will show how it is possible to give a physical characterization of the concept of quantum symmetries described by a nontrivial Hopf algebra. In particular, I will discuss the generalization of the Noether analysis for a scalar field in kappa-Minkowski space-time and derive conserved charges associated with each generator of the kappa-Poincare\' Hopf-algebra. Then I will report on a recent proposal for the quantization of a scalar field enjoying kappa-Poincare\' symmetries, which consists in a construction of the Fock-space of the theory consistent with the structure of deformed symmetries. Finally I will comment on possible applications of deformed symmetries scenarios in cosmology.

Relational particle mechanics are theories of relative angles and relative (ratios of) separations only. These bear a number of resemblances to the geometrodynamical formulation of general relativity and as such are useful analogues for at least some approaches to the notorious problem of time in quantum gravity. I have recently provided a fairly complete study of the configuration spaces of these theories in spatial dimension 1 and 2, am subsequently studying the redused forms of these theories at the quantum level, and this shall provide a number of useful examples for the conceptual discussion of various problem of time strategies

In this talk we propose a Reduced Phase Space Quantization approach to Loop Quantum Gravity. The idea is to combine the relational formalism introduced by Rovelli in the extended form developed by Dittrich and the Brown-Kuchar-Mechanism. The relational formalism can be used to construct gauge invariant observables for constrained systems such as General Relativity, while the Brown-Kuchar-Mechanism is a particular application of the relational formalism in which pressureless dust is taken as the clock of the system. By combining these two we obtain a framework in which the constraints of General Relativity deparametrize such that the algebra of observables has a very simple structure and furthermore we obtain a so called physical Hamiltonian generating the evolution of those observables. The quantization of the reduced phase space and the physical Hamiltonian can be obtained by using standard LQG techniques and gives a direct access to the physical Hilbert space, which is much harder to achieve in the standard Dirac quantization. Additionally we will analyze the quantization in the Algebraic Quantum Gravity context and discuss the differences that occur. Finally we will present recent results where this framework has been applied to cosmological perturbation theory.

In the first part of the talk we introduce a technique to compute large scale correlations in LQG and spinfoam models. Using this formalism we calculate some components of the graviton propagator and of the n-points function. In the second part we apply the ideas suggested by LQG to the black hole interior . The result of the quantum analysis is that the classical singularity disappears in loop quantum gravity. Solving the semiclassical Einstein equation of motion we obtain a metric regular and singularity free in contrast to the classical one. By using the new metric we calculate the Hawking temperature, entropy and we study the mass evaporation process.

There is a deep relation between Loop Quantum Gravity and notions from category theory, which have been pointed out by many researchers, such as Baez or Velhinho. Concepts like holonomies, connections and gauge transformations can be naturally formulated in that language. In this formulation, the (spatial) diffeomorphisms appear as the path grouopid automorphisms. We investigate the effect of extending the diffeomorphisms to all such automorphisms, which can be viewed as \"distributional diffeomorphisms\". We also give a notion of \"categorial holonomy-flux-algebra\", and present the construction of the automorphism-invariant Hilbert space for abelian gauge groups, which will be entirely combinatorial.

I discuss the status of Quantum Gravity Phenomenology, focusing separately on the 3 key areas: ability to discover, ability to constrain, and ability to falsify. And I stress the importance of adopting carefully taylored test theories as a remedy to difficulties encountered when comparing experimental evidence to theory evidence.

I discuss how physics beyond the Planck scale and before inflation might leave an imprint on the primordial spectrum. There are interesting limitations connected with the information paradox that suggests unexpected new ways to test ideas on quantum gravity.