Quantum Gravity

The kinematical framework of canonical loop quantum gravity has mostly been studied in the context of compact Cauchy slices. However many key physical notions such as total energy and momentum require the use of asymptotically flat boundary conditions (and hence non-compact slices). We present a quantum kinematics, based on the Koslowski-Sahlmann representation, that successfully incorporates such asymptotically flat boundary conditions. Based on joint work with Madhavan Varadarajan.

I will describe a proposal for a generalization of the BMS group in which the conformal isometries of the sphere (Lorentz group) are replaced by arbitrary sphere diffeomorphisms. I describe the computation of canonical charges and show that the associated Ward identities are equivalent to the Cachazo-Strominger subleading soft graviton formula. Based on joint work with Alok Laddha.

An algebraic view allows one to compute properties of physical states without having to introduce an explicit Hilbert space. In relational systems without absolute time, a state cannot be completely positive once a choice for a (possibly local) internal time has been made. A more general class of `almost-positive' states is introduced in this talk, together with a discussion of their constrained dynamics.

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions.

Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop.

We  will  briefly review  the  issue  of    "information loss"    during  the Hawking   evaporation of a  black hole,  and  argue that    the  quantum dynamical  reduction  theories, which  have  been  developed to  address the   measurement problem  in quantum mechanics,  possess the  elements to  diffuse the ``paradox”  at the qualitative  and  at   the  quantitative  level, leading to what  seems  to be an overall  coherent  picture.  

Although the inflationary predictions for the primordial power spectrum of    density inhomogeneities   seem  very successful, there is an obscure part in our understanding of the emergence of the seeds of cosmic   structure:  How  does  a universe which at one pint  in time is described by a  state that is fully  homogeneous and isotropic,  evolve into a state that is not,   given that the dynamics  does not  contain any  source  for the  undoing of  such symmetry?   We will  discuss  an   approach that  offers  a resolution  of the  issue  in the context of  proposals to deal  with the measurement  problem in quantum  mechanics. We will  see that the   approach  naturally  resolves the difficulties  raised  by the  lack of  observation of tensor modes.

Path integrals are at the heart of quantum field theory. In spite of their covariance and seeming simplicity, they are hard to define and evaluate. In contrast, functional differentiation, as it is used, for example, in variational problems, is relatively straightforward. This has motivated the development of new techniques that allow one to express functional integration in terms of functional differentiation. In fact, the new techniques allow one to express integrals in general through differentiation. These techniques therefore add to the general toolbox for integration and integral transforms such as the Fourier and Laplace transforms. Here, we review some of these results, we give simpler proofs and we add new results, for example, on expressing the Laplace transform and its inverse in terms of derivatives, results that may be of use in quantum field theory, e.g., in the context of heat traces.

In order to introduce the cosmological constant in a simplicial geometry, constant curvature should be introduced on simplex faces. This yields a compactification of the phase space and the finiteness of the Hilbert for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space.

Quantum effects render black holes unstable.  Besides Hawking radiation there is another, genuinely quantum gravitational, source of instability: the Hajicek-Kiefer explosion via tunnelling to a white hole.  A recent result in classical general relativity makes this decay channel plausible: there is an exact external solution of the Einstein equations locally (but not globally) isometric to extended Schwarzschild, which describes an object collapsing into a black hole and then exploding out of a white hole. The tunnelling time can in principle be computed using Loop Quantum Gravity. If it is sufficiently short, present explosions of primordial black hole could be observables, opening a new observational window on quantum gravity. I discuss the possibility that these explosions could be related to the recently observed and mysterious Fast Radio Bursts. 

By explicit construction, I will show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (Causal) Dynamical Triangulations.

I propose a quantum gravity model in which the fundamental degrees of freedom are pure information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration arising between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension. The model has three quantum phases: a mean field phase in which the spectral and Hausdorff dimensions coincide and are larger then 4. A fluctuations-dominated phase in which the Hausdorff dimension can only be 4 and the spectral dimension is lower than the Hausdorff dimension and a disordered phase in which there is no space-time interpretation. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. An ultraviolet fixed point at the lower critical dimension of the Ising model implies the absence of space-time at very small scales. At finite temperatures the universe emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits also macroscopic black hole configurations corresponding to graphs containing holes with no space time inside and around which there are "Schwarzschild-like horizons" with a lower spectral dimension and an entropy proportional to their surface.