Quantum Gravity

The idea behind an intersection between loop quantum gravity and noncommutative geometry is to combine elements of unification with a setup of canonical quantum gravity. In my talk I will first review the construction of a semi-finite spectral triple build over an algebra of holonomy loops. Here, the loop algebra is a noncommutative algebra of functions over a configurations space of connections, and the interaction between the Dirac type operator and the loop algebra captures information of the kinematical part of canonical quantum gravity. Next, I will show how certain normalizable, semi-classical states are build which connects the spectral triple construction to the Dirac Hamiltonian in 3+1 dimensions. Thus, these states can be interpreted as one-particle fermion states in an ambient gravitational field. This analysis indicates that the spectral triple construction involves matter degrees of freedom.

I will discuss the contribution to black hole thermodynamics from a variation in the cosmological constant. The description of black hole with a cosmological constant is facilitated by introducing a two-form potential for the static Killing field. The resulting Smarr formula then includes a term proportional to the cosmological constant times an effective volume, which arises as the difference between the Killing potential on the horizon and the boundary at infinity. This volume is shown to be equal to the difference between the (infinite) volume of AdS and the (infinite) volume outside the black hole horizon of AdS containing a black hole--and so can be interpreted as the volume occupied by the black hole. I will outline the derivation for the first law for AdS black holes including a variation in the cosmological constant. This yields a new work term, the change in the cosmological constant times the effective volume. Hence this is analogous to a "volume times change in pressure" work term in classical thermodynamics. This suggests that the usual change in mass term is better interpreted as a change in the enthalpy, the mass plus the pressure times the volume. In the AdS/CFT correspondence a change in the cosmological constant corresponds to a change in the t'Hooft coupling, for example, a change in the number of degrees of freedom. The effective volume multiplier then looks like a chemical potential. Members of the audience will be asked to contribute their own interpretations at this point.

As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we analyze the physical consequences of including inhomogeneities. We consider a gravitational model in vacuo which possesses local degrees of freedom, namely, the linearly polarized Gowdy cosmologies. We carry out a hybrid quantization which combines loop and Fock techniques. We discuss the main results of this hybrid quantization, which include the resolution of the cosmological singularity, the construction of the Hilbert space of physical states, and the recovery of a conventional quantization for the inhomogeneities. In addition, an analysis of the model at the effective level confirms the robustness of the Big Bounce scenario, with preservation -or partial amplification- of the amplitudes of the inhomogeneous modes through the bounce in a statistical average.

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.

I comment on rather significant recent developments that are relevant for proposals I had presented in previous PI seminars. The Fermi/GLAST space telescope has reported observations that would naturally fit previous formalizations of Planck-scale-induced in-vacuo dispersion (but also quite a few other things). And the unexplained excess noise found at the GEO600 interferometer is just of the type that had been previously described in terms of phenomenological models of spacetime foam (but may well be caused by quite a few other things). On the pure-theory side I can finally keep my promise to show that spacetime noncommutativity is a valuable tool of exploration of nonclassicality of spacetime, allowing the derivation of discretized spectra of distance, area, volume, and also providing a completely new overall geometric picture, in which amusingly the number Pi looses some of its privileges.

We derive geometric correlation functions in the new spinfoam model with coherent states techniques, making connection with quantum Regge calculus and perturbative quantum gravity. In particular we recover the expected scaling with distance for all components of the propagator. We expect the same technique to be well-suited for other spinfoam models.

In this talk I will review how ideas borrowed from perturbative Quantum Gravity and Effective Field Theory (EFT) in Particle Physics can be applied to problems in General Relativity (GR), such as calculating gravitational wave emission by inspiralling spinning binary systems, including finite size effects and absorption. I will discuss in somewhat more detail how to account for dissipative effects, where the GR/EFT duality is used to predict the power loss due to absorption in the dynamics of binary spinning Black Holes.

In this talk I will describe a topos formulation of consistent histories obtained using the topos reformulation of standard quantum mechanics put forward by Doering and Isham. Such a reformulation leads to a novel type of logic with which to represent propositions. In the first part of the talk I will introduce the topos reformulation of quantum mechanics. I will then explain how such a reformulation can be extended so as to include temporally-ordered collection of propositions as opposed to single time propositions. Finally I will show how such an extension will lead to the possibility of assigning truth values to temporal propositions.

The handling of the constraints on initial data is a major issue in most canonical formulations of general relativity. Since the 1960s unconstrained initial data for GR that living on null hypersurfaces has been known, but no canoncial formulation based on these data was developed due to conceptual and technical difficulties. I will explain how these dificulties have been overcome and outline the resulting canonical framework. I will also explain how this might be the ideal setting to attempt a proof of the Bousso entropy bound, or to incorporate the associated holographic principle in a quantization of gravity.

Using 2-dimensional CGHS black holes, I will argue that information is not lost in the Hawking evaporation because the quantum space-time is significantly larger than the classical one. I will begin with a discussion of the conceptual underpinnings of problem and then introduce a general, non-perturbative framework to describe quantum CGHS black holes. I will show that the Hawking effect emerges from it in the first approximation. Finally, I will introduce a mean field approximation to argue that, when the back reaction is included, future null infinity is `long enough\' to capture full information contained in pure states at past null infinity and that the S-matrix is unitary. There are no macroscopic remnants.

As well known, cosmic ray experiments can put strong constraints on possible Lorentz Invariance Violations. In particular, the presence of the so called GZK \'cut-off\' may indicate that protons do propagate in the Universe as expected from relativistic invariance. The presence of this feature in the spectrum has been convincingly indicated by the HiRes and Auger experiments, while the Auger Observatory has given indication on the correlation of Ultra High Energy Cosmic particles with nearby sources, as predicted by the GZK feature. I review the experimental results and discuss in particular both the theoretical and experimental intricacies and the limits on LIV parameters that can be deduced.