General Relativity & Quantum Cosmology

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.

Improving the broadband quantum sensitivity of an advanced gravitational wave detector is one of the key steps for future updating of  gravitational wave detectors. Reduction of the broadband quantum noise needs squeezed light with frequency dependent squeezing angle. Current designs for generating frequency dependent squeezed light are based on an ultra-high finesse filter cavity, therefore optical loss will serious contaminate the squeezed light. To circumvent this problem, we  propose an new method for generating a frequency dependent squeezing of quantum noise field quadrature by engineering the quantum entangled field pairs which are filtered through the interferometer arm cavity.  This new method may have the potential to beat the quantum noise by 7dB in recent future.

Questions of nonlinear stability in global AdS space have recently received a significant amount of attention, both as an interesting problem in mathematical general relativity and nonlinear dynamics, and in relation to thermalization studies within the AdS/CFT paradigm. Working with nonlinear perturbation theory (the main technique available for analytic studies in this area) requires a thorough understanding of the properties of linearized AdS fields'

mode functions, which are the fundamental building blocks in perturbative treatments of nonlinearities. While complicated explicit expressions for these mode functions are available in the literature, they hide a good deal of the elegant underlying structure dictated by the AdS symmetries. Extending the mode functions in the flat embedding space (in which the AdS space can be realized as a hyperboloid) results in families of homogeneous polynomials, on which the AdS isometries act in a straightforward manner. This suggests a simple proof of important selection rules in nonlinear perturbation theory.

Studies of multiplet structures of the mode functions furthermore reveal a relation to the Higgs oscillator, a well-known quantum-mechanical superintegrable system. This AdS connection leads to an explicit construction of the hidden symmetry generators for the Higgs oscillator, a long-standing problem in mathematical quantum mechanics.

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.

Current observations provide precise but limited information about inflation and reheating. Theoretical considerations, however, suggest that the early universe might be filled with a large number of interacting fields with unknown interactions.  How can we quantitatively understand the dynamics of perturbations during inflation and reheating in such scenarios and when only limited

constraints are available from observations?   Based on a precise

mapping between particle production in cosmology to resistivity in disordered, quasi one-dimensional wires, I will provide a statistical framework to resolve such seemingly intractable calculations. A number of phenomenon in disordered wires find an analogue in particle production. For example, Anderson localization in quasi one-dimensional wires can be directly mapped to exponential particle production in the early universe. The talk will be focussed on the general framework and some toy examples, though in the end I will discuss possible (future) applications to calculating observables.