General Relativity & Quantum Cosmology

We expect certain universal results in classical gravity to come unaltered from a quantum theory of gravity. In this talk, I will firstly discuss new ideas on this topic, and the latest understanding we have on this, in an accessible way. After that, I will focus on local symmetries in gravity, and obtain the most general off-shell algebra of diffeomorphisms that acts non-trivially at corners, where gauge charges are supported. Noether charges in Einstein gravity are then shown to generate a faithful representation of this algebra. After pausing and reviewing the covariant phase space formulation, explaining the questions and issues our community faced in successfully applying it to gravity, I will show how a careful treatment of embeddings allows us to establish a field space where Noether charges act canonically via Poisson bracket. This solves a longstanding puzzle in this field, opening doors to new promising investigations. I will conclude by mentioning them and commenting on how new proposals might shed light on old unanswered questions in quantum gravity.

Zoom Link: https://pitp.zoom.us/j/96552295909?pwd=cFZwcGxLdWlaWWhRS21RMExUd1RjQT09

I study the dynamics of a gyroscope far from an isolated source of gravitational waves. With respect to a local frame 'tied to the distant stars', the gyroscope precesses when gravitational waves cross its path, resulting in a net `orientation memory', carrying information on the gravitational wave profile. I show that the precession rate is given by the so-called "dual covariant mass aspect", providing a celestially local measurement protocol for this quantity. Moreover, I show that the net memory effect can be derived from the flux-balance equations for superrotation charges in the "generalized BMS" algebra. Finally, I show how the spin memory effect à la Pasterski et al. is reproduced as a special case.

Guided by the principles of effective field theory (EFT), I will discuss three avenues to constrain physics beyond General Relativity with black-hole observations.

1) Shadows: Without specifying any particular gravitational dynamics, I will discuss image features of black-hole shadows in general parameterizations and their relation to fundamental-physics principles like (i) regularity (no remaining curvature singularity), (ii) simplicity (a single new-physics scale), and (iii) locality (a new-physics scale set by local curvature).

2) Stability: Specifying the linearized dynamics around black-hole spacetimes determines the onset of potential instabilities and connects to the ringdown phase of gravitational waves. I will delineate how said instabilities can constrain the EFT of gravity, theories of low-scale dark energy, as well as ultralight dark matter.

3) Nonlinear evolution: The larger the probed curvature scale, the tighter the constraints on new gravitational physics. Making full use of experimental data, thus relies on predictions in the nonlinear regime of binary mergers. I will present recent progress towards achieving stable numerical evolution for the EFT of gravity up to quadratic order in curvature.

Zoom Link: https://pitp.zoom.us/j/98276687334?pwd=UnM2dElacWNtempQUHJMNVlaNHgyUT09

Conformal field theories have played an important role in understanding the origin of gravitational entropy, as the Cardy formula accounts for the entropy of three-dimensional BTZ black holes or black holes with an AdS3 near-horizon region. More recently, Cardy-type formulas have also been derived for different field theories, such as warped conformal field theories, which are two-dimensional field theories invariant under chiral scaling symmetry.

In this talk I discuss a particular class of three-dimensional spacetimes, dubbed warped flat spaces. I will present their geometric and thermodynamic properties, focusing on their causal structure. I will explain how their entropy can be accounted for through a dual description in terms of a warped conformal field theory.

For quantum gravity states associated to open spin network graphs, we study how the boundary (the set of open edges, which carries spin degrees of freedom) is affected by the bulk, specifically by its combinatorial structure and by the quantum correlations among the intertwiners. In particular, we determine under which conditions certain classes of quantum gravity states map bulk degrees of freedom into boundary ones isometrically (which is a necessary condition for holography). We then look at the entanglement entropy of the boundary and recover, for slightly entangled intertwiners, the Ryu-Takayanagi formula with corrections induced by the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound, a mechanism which thus leads to the rise of a black hole-like region in the bulk.

Zoom Link: https://pitp.zoom.us/j/96356007543?pwd=U2VrRlhyOThMODdMYllDMnB6VjlZQT09

The era of multi-messenger astronomy is well and truly upon us, with 90 compact binaries observed since the Advanced LIGO detectors saw first light in 2015. Despite our very own cosmic backyard, the Milky Way, being ripe with prospective sources for ground-based gravitational wave detectors, the closest source detected thus far (GW170817, the famed binary neutron star merger) was at a distance of 40 Mpc. In this talk, I will outline a number of prospective Galactic multi-messenger sources, and discuss several ways in which their detection over the next twenty years can be improved through both experimental and analytical techniques. 

Zoom Link: https://pitp.zoom.us/j/93664322641?pwd=VUoxbmFGZE1KczJ1RU1MR09TQ05Ldz09

The main feature of tensor models is their melonic large N limit, leading to applications ranging from random geometry and quantum gravity to  many-body quantum mechanics and conformal field theories. However, this melonic limit is lacking for tensor models with ordinary representations of O(N) or Sp(N). We demonstrate that random tensors with sextic interaction transforming under rank-5 irreducible representations of O(N) have a melonic large N limit. This extends the recent proof obtained for rank-3 models with quartic interaction. After giving an introduction to random tensors, I will present the main ideas of our proof relying on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs.

Zoom Link: https://pitp.zoom.us/j/94691275506?pwd=RGFaN0NZR0FScFdOTXFzeFVXaXUvUT09

Accurate waveform models are crucial for gravitational-wave (GW) data analysis, and since numerical-relativity waveforms are computationally expensive, it is important to improve the analytical approximations for the binary dynamics. The post-Newtonian (PN) approximation is most suited for describing the inspiral of comparable-mass binaries, which are the main sources for ground-based GW detectors. In this talk, I discuss a method for deriving PN results valid for arbitrary mass ratios from first-order self-force results, by exploiting the simple mass dependence of the scattering angle in the post-Minkowskian expansion. I present results for the spin-orbit dynamics up to the fourth-subleading PN order (5.5PN) and the spin-spin dynamics up to the third-subleading PN order (5PN). I also discuss implications for the first law of binary mechanics.

Zoom Link: https://pitp.zoom.us/j/92861625861?pwd=cHpXUlM1d01pc09mNGhhQVZxRHBiQT09

This talk focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-j Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to e^{i I}, where I is the Regge action of the geometry plus corrections of higher order in curvature. As a result, the spinfoam amplitude reduces to an integral over Regge geometries weighted by e^{i I} in the semiclassical regime.  As a byproduct, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity.

Zoom Link: https://pitp.zoom.us/j/93699343757?pwd=RnpFeitaTU5qTktzNjlXQW45K1gvQT09

Quantum groups are the proper tool to describe quantum gravity in three dimensions. Several arguments suggest that 2-groups should be used to formulate four dimensional quantum gravity. I will review these motivations and will discuss in particular how 2-groups can be used to extend the definition of a phase space associated to a triangulation or to modify the notion of group field theory to generate topological models. I will also highlight how the kappa Poincaré deformation arises in the 2-group context.

Mergers of compact objects are among the most violent events in the Universe. At close separations, compact binaries emit gravitational waves, releasing enormous amounts of energy until they merge. When matter is present in the system, the event might be accompanied by electromagnetic emission, which can span the entire electromagnetic spectrum. Multi-messenger observations by gravitational-wave detectors and electromagnetic telescopes have opened a new avenue to understand the nature of spacetime and its interaction with matter. In this talk, I will discuss recent efforts to connect first-principle calculations with the electromagnetic radiation emitted in compact binary mergers through general-relativistic magnetohydrodynamic simulations. In particular, I will focus on the relativistic outflows produced in binary neutron star systems and on electromagnetic signatures of supermassive binary black-hole mergers.