General Relativity & Quantum Cosmology

I will present and motivate a program establishing, in full generality, the symmetries and charge analysis for gravitational theories near a generic null hypersurface without specifying any boundary condition.  I will illustrate the first steps of this program on three dimensional Einstein gravity. In this case, there are three charges which are generic functions over the codimension one null surface. The integrability of the charges and the charge algebra depend on the state-dependence of symmetry generators which is a priori not specified. I will establish the existence of infinitely many choices that render the surface charges integrable. Then, I will argue that one expects this result to be valid for d > 3 when there is no Bondi news by developing some aspects of the four dimensional case. Finally, I will put our results in the context of earlier constructions of near horizon symmetries.  

Based on: arxiv:2002.08346, arxiv:2005.06936 and arxiv:2007.12759
 

Dual gravitational charges (DGCs) have been originally computed in the first-order formalism by means of covariant phase space methods using tetrad variables. I show i) why DGCs do not arise using the metric variables and ii) how they can be set to zero by exploiting the freedom to add exact 3-forms to the symplectic potential.

Without exploiting that freedom, DGCs can be understood as Hamiltonian charges associated to the Kosmann variation. I then discuss the implications of this observation for asymptotic symmetries and comment about subleading contributions thereof.

Finally, I also show that DGCs can be equally derived by means of cohomological methods. In this case, DGCs depends on the order of the Lagrangian: they exist only in the first-order formalism.

Millisecond Pulsars (MSPs) have become reliable and
extremely stable workhorses of modern astronomy and physics.  The
North American Nanohertz Observatory for Gravitational Waves, or
NANOGrav, has been observing growing numbers of these systems for over
15 years, and the data look great.  High precision timing of almost 80
MSPs has provided unprecedented sensitivity to the gravitational wave
Universe at nHz-frequencies, where our upper limits are already
constraining the population of super-massive black hole binaries.  But
our sensitivity is increasing each year as we continue to add MSPs to
our timing array and develop new techniques to remove systematics due
to the interstellar medium and the uncertain solar system ephemerides.
Meanwhile, though, our observations provide a wide variety of
astrophysics, such as new neutron star mass measurements and
constraints of the dense matter equation of state.

I will discuss the recent Hamiltonian derivation of dual BMS charges at null infinity using the first order formalism.  More generally, I will discuss how this idea can be used to classify asymptotic charges in gravity.

Extreme-mass-ratio inspirals (EMRIs) are the only gravitational-wave sources for the future LISA detector that combine the issue of strong-field complexity with that of long-lived signals. The result is a profoundly difficult inverse problem, with many theoretical and computational challenges presented both by the forward modeling of the predicted EMRI waveform, and by the recovery of an inverse solution for the presence and properties of actual EMRI signals in LISA data. I outline recent progress and ongoing work on both fronts. Specifically, I describe: i) the next generation of accurate, efficient and extensive models for (the response of LISA to) an EMRI signal; and ii) a heuristic study of degeneracy in the space of LISA-observable EMRIs, with a view to informing analysis strategies for EMRI search and characterization.

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, I will introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. I will show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. I will provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

I discuss general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be non-classical. Remarkably, the argument does not assume any classical or quantum formalism to describe the mediating physical system: the result follows from general information-theoretic principles. This argument provides a robust and general theoretical basis for recently proposed tests of non-classicality in gravity, based on witnessing gravitationally-induced entanglement in quantum probes.

The astrophysical background of gravitational waves (AGWB) is composed by the incoherent superposition of gravitational wave signals emitted by resolved and unresolved astrophysical sources from the onset of stellar activity until today. In this talk, I  will present a theoretical framework  to characterize the AGWB in terms of energy density and polarization and  I will show predictions for the angular power spectra of the background anisotropy and for its cross-correlations with electromagnetic observables, in the frequency bands accessible by  LIGO/Virgo and  LISA.  I will then discuss the astrophysical content of these observables, give an overview of the state of the art of observations, and highlight future observational challenges.

Renormalisation in curved spacetimes is an involved subject. In contrast to renormalisation in a flat spacetime, the standard momentum representation is not directly available. Nevertheless, the momentum dependence of correlation functions is crucial to deciding whether a theory is unitary and causal. I will discuss how to define a notion of momentum dependence in gravity on a fundamental level. With this at hand, one can discuss an important quantum field theory observable: scattering cross sections. Taking the example of gravity-mediated scalar scattering, I will discuss conditions that a quantum field theory of gravity has to fulfil to have a well-behaved scattering amplitude. These can be satisfied without the introduction of massive higher spin modes as is done in string theory. Finally, I will review the status of first principle calculations of the non-perturbative momentum dependence of quantum gravity correlation functions.

Gravitational waves from the coalescence of compact binaries provide a unique opportunity to test gravity in strong field regime. In particular, the postmerger phase of the gravitational signal is a proxy for the nature of the remnant.

This is of particular interest in view of some quantum-gravity models which predict the existence of horizonless dark compact objects that overcome the paradoxes associated to black holes. Such dark compact objects can emit a modified ringdown with respect to the black hole case and late-time gravitational wave echoes as characteristic fingerprints.

In this talk, I develop a generic framework to the study of the ringdown of dark compact objects and provide a gravitational-wave template for the echo signal. Finally, I assess the detectability of dark compact objects with current and future gravitational-wave detectors.

The Raychaudhuri equation predicts the convergence of geodesics and gives rise to the singularity theorems. The quantum Raychaudhuri equation (QRE), on the other hand, shows that quantal trajectories, the quantum equivalent of the geodesics, do not converge and are not associated with any singularity theorems. Furthermore, the QRE gives rise to the quantum corrected Friedmann equation. The quantum correction is dependent on the wavefunction of the perfect fluid whose pressure and density enter the Friedmann equation. We show that for a suitable choice of the wavefunction this term can be interpreted as a small positive cosmological constant.