Quantum Gravity

At the classical level, one can restrict a spherically symmetric model to the corresponding LTB sector by requiring that a so-called LTB condition is satisfied. In this talk we will discuss how this can be generalised in the context of effective models containing quantum gravity inspired modifications of  the classical theory in the form of polymerisations. The formalism presented allows us to consider more general polymerisations than in previous work in the literature. Applications of this framework are then considered, focusing on a particular class of models that have the property that the effective dynamics is completely decoupled along the radial direction. Examples of effective models that fall into this class are discussed and their physical properties are compared with existing models in the literature.

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I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the structure of the Standard Model with asymptotically safe gravity, and the recent first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton. Overall, I will display the progress towards the computation of the quantum effective action which encapsulates effective field theory in the IR limit and the asymptotic safety regime in the UV limit.

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We show that the Ryu-Takayanagi (RT) formula, originally introduced to compute the entropy of a holographic boundary CFT, can be interpreted as entropy of an algebra of bulk gravitational observables. In particular, we show that any Euclidean gravitational path integral satisfying a simple and familiar set of axioms defines type I von Neumann algebras of bulk observables acting on closed codimension-2 asymptotic boundaries. The entropies associated to these algebras, defined via the gravitational path integral, can be written in terms of standard density matrices and standard Hilbert space traces, and in appropriate semiclassical limits are computed by the RT formula with quantum corrections. Our work thus provides a bulk state-counting interpretation of the Ryu-Takayanagi entropy. Since our axioms do not severely constrain UV bulk structures, they may be expected to hold equally well for successful formulations of string field theory, spin-foam models, or any other approach to constructing a UV-complete theory of gravity.

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Extended BMS symmetry is believed to be a fundamental symmetry of any classical gravitational scattering process, as well as of the quantum gravity S-matrix. We explore this property using the BRST formulation of BMS symmetry, which allows to construct a non trivial solution of the Wess-Zumino consistency condition at the null boundaries of spacetime. We interpret this solution as an anomaly for asymptotic BRST Ward identities for superrotations. By relating them to the leading and subleading soft graviton theorem, we recover the well known results that the leading soft theorem is exact at all loop in perturbation theory without ever referring to Feynman diagrams, while the anomaly for superrotations is at the origin of the 1-loop correction to the subleading soft factor. This construction provides a rigorous, fully quantum origin for the invariance of the S-matrix under asymptotic symmetries.

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When the spacetime metric is regarded as a quantum field, the classical trajectories of freely falling objects are subject to random fluctuations, or “noise”. This fundamental noise might even be observable at gravitational wave detectors: if detected, it would provide experimental evidence for the quantization of gravity. The effect of the quantum-gravitational noise is to turn the classical geodesic deviation equation into a stochastic, Langevin-like equation. Moreover, when these results are extended to congruences of geodesics, the quantum fluctuations of spacetime give rise to an additional term in the Raychaudhuri equation with the same sign as the other terms.

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