Quantum Gravity

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, $\Lambda = 0$. However, there is no physically useful notion of asymptotics for the universe we inhabit with $\Lambda > 0$. The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation.

The possibility of observing quantum gravitational phenomena, viewed as remote until not long ago, is increasingly considered to be plausible.  A potentially observable phenomenon is the decay of black holes via a quantum gravitational tunneling akin to standard nuclear decay.  Loop quantum gravity can be used to compute the corresponding lifetime.  This could be much shorter than the Hawking radiation time, rendering the effect astrophysically relevant. Preliminary estimates indicate that centimeter-size primordial black holes should be exploding today and predict impulsive high energy as well as microwave signals tantalizing similar to the Fast Radio Bursts recently observed by the Areceibo and Parkes radio telescopes.  The predicted signal has a characteristic distance/frequency relation which will allow to test the Planck star hypotheses in the near future.

We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with Forman weighted combinatorial curvatures and simplicial volumes relying on a decomposition of an abstract simplicial complex into realized embeddings of proper skeletons, we demonstrate model phenomenology such as a minimal volume-scale cutoff, a positive-definite cosmological constant as a regulator for non-degenerate geometries, and naturally emergent simplicial structures from Metropolis network evolution simulations with no restrictions on attachment rules or regular building blocks. Properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity will also be illustrated. We conclude with prospects for future investigations into the model, discussing ongoing simulations, modifications to the structure of the theory, and broader applications of the framework.

General relativity is invariant under diffeomorphisms, and

excitations of the metric corresponding to diffeomorphisms

are nonphysical.  In the presence of a boundary, though --

including a boundary at infinity -- the Einstein-Hilbert

action with suitable boundary terms is no longer fully

invariant, and certain diffeomorphisms are promoted to

physical degrees of freedom.  After briefly describing how

this happens in (2+1)-dimensional AdS gravity, I will

report on work in progress on the asymptotically flat case,

for which the newly dynamical diffeomorphisms are the

superrotations, and the boundary action is related to

coadjoint orbits of the Virasoro group and Hill's equation.

We present results from a study of Euclidean dynamical triangulations in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior, and that once this tuning is performed, our simulations provide evidence in support of the asymptotic safety scenario for gravity.  We discuss our motivation for the tuning and present our numerical results. Finally, we discuss what our simulations imply for the dimension of the ultraviolet critical surface, which sets the number of free parameters in the theory.

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.