General Relativity & Quantum Cosmology

Higher-curvature gravity can offer UV completions of GR, but generically suffers from 4th-order propagating degrees of freedom often spoiling unitarity, e.g. Stelle gravity. Recently it was noticed that “Einsteinian gravities” allow for higher curvature interactions match Einstein’s spectrum at the linearised level, avoiding the dangerous 4th-order propagating degrees of freedom. We investigate the renormalisation group flow of Einstein cubic gravity couplings and identify the entire phase diagram of the theory, showing that Einstein cubic gravity remains ghost-free in the quantum regime. To tackle questions of unitarity and causality directly, we make a Lorentzian computation of the asymptotically safe graviton propagators of the transverse-traceless and scalar mode. We showed that beyond the requirement of using a causality-preserving regulator, such as Callan-Symanzik, setting up differential equations for coupled spectral functions must satisfy additional constraints related to diffeomorphism and BRST symmetry. We found three avenues to solve the coupled system of running Kallen-Lehmann spectral representations, leading to 1-loop exact spectral functions which are compatible with causality and unitarity. Furthermore, they provide the first direct asymptotically safe predictions to the full quantum propagators, the corresponding Weyl-tensor and Ricci-scalar form factors in the quantum effective action.

We study subregion algebras in classical and perturbative quantum gravity on half-spaces of event horizons. We construct half-sided supertranslation generators by extending subregion phase spaces of the event horizon to include doubled pairs of edge modes obtained from splitting the horizon. These edge modes carry a corner symplectic form that gives rise to canonical generators of half-sided boosts and translations, the former of which is the area operator at the corner while the latter corresponds to null time evolution along the horizon. The charges act nontrivially on gravitationally dressed bulk observables, such that subalgebras take the form of a crossed product by the associated automorphism group. Quantizing the extended phase space after linearizing around a black hole, we obtain for each cut a Type II$_{\infty}$ von Neumann algebra whose entropy coincides with the generalized entropy of that cut. The nesting property of the resulting one-parameter family of subalgebras implies a generalized second law for linearized perturbations of Killing horizons. Finally, we use gravitational half-sided modular inclusion algebras to prove quantum focusing along Killing horizons in the perturbative quantum gravity regime.

I will revisit the canonical quantization of General Relativity in the self-dual formulation in the presence of a cosmological constant, discussing the normalizability of graviton states over the de Sitter spacetime. Time permitting, I will explain how the physics of the Hamiltonian constraint is analogous to the quantum Hall effect, with the cosmological constant playing the role of a quantum gravitational Hall resistivity.

Small naked singularities—those not shielded by a macroscopic event horizon—are ubiquitous in classical General Relativity. Their existence constitutes apparent violations of the weak cosmic censorship conjecture, which asserts that physically reasonable solutions should appear regular to asymptotic observers. In this talk, we will show how the inclusion of stringy and quantum effects resolves these pathologies by uplifting naked singularities into fully regular configurations. Focusing on critical gravitational collapse as a concrete example, we demonstrate that a proper quantum treatment replaces naked singularity formation with black hole formation. This suggests that cosmic censorship is not fundamentally a property of classical General Relativity, but rather emerges only once quantum gravitational effects are taken into account.

In this talk, I will argue that the universal structure of the corner algebra offers a new perspective on quantum gravity, in which the representation theory of this algebra plays a role as fundamental as that of the Poincaré algebra in quantum field theory. I will discuss the representation theory of the (quantum) universal and extended corner symmetries in a simplified model of spherically symmetric spacetimes, where the corner reduces to a point and the algebra correspondingly simplifies. Furthermore, I will propose a purely algebraic procedure for gluing regions in the quantum theory, compute the entanglement entropy, and derive the entropy–area law for a class of specific coherent states.