General Relativity & Quantum Cosmology

Incorporating time poses a challenge for all quantum gravity programs primarily build around Euclidean spacetimes. This talk surveys how the gravitational asymptotic safety program may address this challenge by encoding the gravitational degrees of freedom via the Arnowitt-Deser-Misner (ADM) decomposition of the spacetime metric. This formulation equips spacetime with a foliation structure singling out a preferred direction. This structure may then take the role of time in the Lorentzian framework. Within this setting, we will outline recent results related to the Wilsonian renormalization group flow of the graviton two-point function including the infrared attractors rendering the graviton massless. Furthermore, we will explain how these results generalize to Lorentzian signature spacetimes and briefly comment on potential applications in the context of cosmology.

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Zoom link https://pitp.zoom.us/j/98382991491?pwd=SmtpMTRTK2NUMEpuN3laa0pIWWs2UT09

Spinning supermassive black holes (BHs) in active galactic nuclei (AGN) can launch relativistic collimated outflows, or jets, by coiling up the magnetic field lines that cross the event horizon on the scale of BH gravitational radius, Rg. Sustained jet launching and propagation to kpc-scales are thought to require non-zero angular momentum to form an accretion disk, keep the magnetic field lines on the BH, and ensure stable jet propagation. Past 3D general relativistic magnetohydrodynamic (GRMHD) work predicted that absent gas angular momentum, magnetized jets are expected to become unstable to the kink instability already at 800 Rg, i.e., orders of magnitudes smaller distances than the BH sphere of influence, or the Bondi radius, RB (e.g., for Sgr A* and M87, RB~10^[5-6] Rg). This raises the question: Do the jets need gas angular momentum to survive the kink instability and make it out to large distances, outside of Rb? I will present 3D GRMHD simulation results for a rapidly spinning BH immersed into uniform zero angular momentum gas threaded by a weak vertical magnetic field, with the largest simulated Bondi radius to date, RB = 1000 Rg. I will show that the BH accumulates dynamically-important magnetic field, enters the magnetically-arrested disk state, and produces powerful jets that make it out of Rb. I will also show how the jets get twisted into knots and dissipate their energy after the MAD state ends.

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Zoom link https://pitp.zoom.us/j/99925612004?pwd=QkhIUmpKRkVKUURpclhPekJST2NIQT09

Group field theory (GFT) is a background independent approach to quantum gravity in which the quanta represent "building blocks of space". It has been successfully applied to the cosmological setting and shown to have the potential for rich phenomenology. In this talk we will explore a novel proposal to construct operators in GFT based on symmetries of the action, which can then be identified with respective classically conserved currents. This construction relies on a relational coordinate system spanned by four massless scalar fields. As the classical currents are related to the components of the metric, the expectation values of the new GFT operators can be interpreted as giving rise to an effective metric originating directly from the quantum theory. We proceed to investigate the implications of this proposition for a flat homogeneous universe and its perturbations.

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Zoom link https://pitp.zoom.us/j/98843634192?pwd=OWs1SEdiWnIyYmlSbTh3bU9MaDBDdz09

In this talk I will present our 3+1 formulation of the Four-Derivative scalar-tensor theory of gravity with a modified puncture gauge that proves to be well-posed. Then I will show the results from Binary Black Hole evolutions that we have obtained from the implementation of these equations with GRFolres, the extension for modified gravity of our numerical relativity code GRChombo.

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Zoom link https://pitp.zoom.us/j/96339156414?pwd=ajhWb1hQNFRYalRpUEd3ajhYdTFldz09

It is a general expectation in several approaches to quantum gravity that continuum physics emerges as a macroscopic phenomenon from the collective behavior of fundamental quantum gravity degrees of freedom. However, a physical understanding of this emergence process requires us to address deeply intertwined technical and conceptual issues. In this talk, I will focus on two of them: the localization problem, related to the background independence of the underlying quantum gravity theory, and the coarse-graining problem, related to the extraction of the macroscopic, continuum physics from the microscopic, quantum-gravitational one. After discussing what strategies can be adopted in general to address these issues, I will show a concrete implementation of such strategies in the context of the group field theory approach to quantum gravity. I will then demonstrate how these strategies can be employed to extract cosmological physics from group field theories, allowing to clarify the intrinsically quantum-gravitational nature of cosmic structures and to characterize the impact of quantum gravity effects on the emergent cosmological dynamics.

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Zoom link https://pitp.zoom.us/j/99070866809?pwd=Y1VGdGR5clZ0bTFwY2dBRHBwU3ptUT09

Gravitational waves have uncovered a treasure trove of nearly 90 merging black holes and neutron stars, each with its own unique story to tell. In the first part of the talk, our focus will center on black hole spins, seeking to decipher the secrets hidden within, including their origins, hometowns, and the forces driving their mergers. We will challenge the belief that isolated binary black holes should have spins aligned with orbital angular momentum. We will explore the mechanisms influencing these spins, from their origins to the forces driving their mergers.

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Zoom link https://pitp.zoom.us/j/95680635803?pwd=Yll6NjFPbmpMZ1lTS0JtdUp6dG1RZz09

Superradiant instabilities may create clouds of ultralight bosons around rotating black holes, forming so-called "gravitational atoms". The presence of a binary companion can induce transitions between bound states of the cloud ("resonances"), as well as from bound to unbound states ("ionization"). These processes backreact on the binary dynamics and leave characteristic imprints on the emitted GWs, carrying direct information about the mass of the boson and the state of the cloud. Even though some of the resonances can destroy the cloud before the system becomes observable in GWs, their backreaction forces the binary inclination towards attractors, opening up the possibility to infer the existence of the boson from a statistical analysis of a population of binary black holes. We also discuss implications for eccentric orbits and merger rates

In this presentation, I will discuss two distinct topics, one relating to the foundational aspects of LQG and the other concerning its applicational implications.
Firstly, I will explore the U(1)^3 model of Euclidean Quantum Gravity, which serves as an interesting testing ground for the dynamics problem in LQG. With its analogous constraint structure to full gravity, the U(1)^3 model may hold the key to enhanced quantization techniques.

Secondly, I will delve into the asymptotic symmetries of General Relativity in the Ashtekar-Barbero formulation. New parity conditions for the Ashtekar-Barbero variables will be proposed, which do produce non-trivial supertranslation charges at spatial infinity. This development paves the way for investigating the quantum characteristics of supertranslation charges within the context of LQG.

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Zoom link https://pitp.zoom.us/j/99532986538?pwd=cnU0VnpJbjU4TSt4MEEzVngxb2wvdz09

According to the Belinski-Khalatnikov-Lifshitz conjecture, the Bianchi IX spacetime describes the evolution of each spatial point close to a generic spacelike singularity. However, near the singularity, quantum effects are expected to be relevant. Therefore, in this work a quantum analysis of the model is performed, mainly focusing on its chaotic nature. Considering some minimal approximations, it is possible to encode all the information of the quantum degrees of freedom in certain canonical variables, expanding thus the classical phase space. In this way, we can apply the usual methods of dynamical systems for studying chaos. In particular, two techniques are considered. On the one hand, an analytical study is carried out, which provides an isomorphism between the quantum dynamics of Bianchi IX and the geodesic flow on a Riemannian manifold. On the other hand, by means of numerical simulations, the fractal dimension of the boundary between points with different outcome in the space of initial data is studied. The main conclusion is that, although the quantum system is chaotic, the quantum effects considerably reduce this behavior as compared to its classical counterpart.

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Zoom link https://pitp.zoom.us/j/91559466008?pwd=UzQvTGRkR3VQWm9MWDlaaVAyNi9EQT09

In the quest to understand the fundamental structure of spacetime (and subsystems) in quantum gravity, it may be worth exploring the ultimate consequences of non-perturbative canonical quantization, carefully taking into account the constraints and gauge invariance of general relativity. As the reduced phase space (or even the pre-phase space) of gravity lacks a natural linear structure, a generalization of the standard method of quantization (based on global conjugate coordinates) is required. One such generalization is Isham's method based on transitive groups of symplectomorphisms, which we test in some simple examples. In particular, considering a particle that lives on a sphere, in the presence of a magnetic monopole flux, we algebraically recover Dirac's charge quantization condition from a "Casimir matching principle", which we propose as an important tool in selecting natural representations. Finally, we develop the non-perturbative reduced phase space quantization of causal diamonds in (2+1)-dimensional gravity. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$. Applying Isham's quantization we find that the Hilbert space of the associated quantum theory carries a (projective) irreducible unitary representation of the $BMS_3$ group. From the Casimir matching principle, we show that the states are realized as wavefunctions on the configuration space with internal indices in unitary irreps of $SL(2, \mathbb{R})$. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the boundary length.

Papers on quantization of causal diamonds:
https://arxiv.org/abs/2308.11741
https://arxiv.org/abs/2310.03100

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Zoom link https://pitp.zoom.us/j/98636934234?pwd=THBCcFpYWHYzWmY0YjViY3Q1a3VYdz09

Recently, models with different properties have been proposed for polymerized dust collapse and regular black holes. To fully understand their properties and differences, we provide a systematic procedure to construct effective polymerized spherically symmetric models encoding holonomy corrections as $1+1$d field theory from effective regular cosmological dynamics or stationary effective metrics. We apply this formalism and consider models that have the following advantages: The effective dynamics can be derived from a class of extended mimetic gravity Lagrangians in 4 dimensions. The models admit a consistent Lemaitre-Tolman-Bondi (LTB) condition, by which the dynamics is completely decoupled along the radial direction in LTB coordinates, trivializing the junction condition in dust collapse. The class of effective dynamics admits a polymerized Birkhoff-like theorem, which leads to a stationary effective metric in the polymerized vacuum. The effective dynamics can reproduce known regular black hole solutions, including Bardeen and Hayward, by a suitable choice of holonomy corrections. As a concrete example, we construct an effective model compatible with the improved dynamics of loop quantum cosmology in the decoupled LTB sector. We compare it with several effective polymerized models recently introduced in the context of loop quantum gravity and gain some new insights into the presence of shocks.

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Zoom link https://pitp.zoom.us/j/99966795418?pwd=Ty9mRXNML3NsUXdvcU1WUTdCaWpVZz09

Extreme mass-ratio binary black hole systems, known as EMRIs, are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). We hope to use these systems to probe black hole spacetimes in exquisite detail and make precision measurements of supermassive black hole properties. Accurate models using general relativistic perturbation theory will allow us to unlock the potential of these unique systems. Such models must include post-geodesic corrections, which account for forces driving the smaller black hole away from a geodesic trajectory. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime, introducing post-geodesic correction called the spin-curvature force. In this talk, I will present our calculation of EMRI waveforms that include both spin-curvature forces and the leading backreaction due to gravitational radiation. We use a near-identity transformation to eliminate dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies; such efficiency is crucial for LISA data analysis. Finally, I will discuss what aspects still need to be included in future calculations so that we can use EMRIs for a new era of precision gravitational-wave astronomy, addressing outstanding puzzles in astrophysics, cosmology and fundamental theoretical physics.

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Zoom link https://pitp.zoom.us/j/91917788358?pwd=MWp5OUhxbkRmZDFxWWE4cHR0VlBTUT09