General Relativity & Quantum Cosmology

Gibbons and Hawking proposed that the Euclidean gravity path integral with periodic boundary conditions in time computes the thermal partition sum of gravity. As a corollary, they argued that a derivative of the associated free energy with respect to the Euclidean time period computes gravitational entropy. Why is this interpretation correct?  That is, why does this path integral compute a trace over the Hilbert space of quantum gravity?   I will show that the quantity computed by the Gibbons-Hawking path integral is equal to an a priori different object -- an explicit thermal trace over the Hilbert space spanned by states produced by the Euclidean gravity path integral. I will explain that this follows if the Hilbert space with two boundaries factorizes into a product of two single boundary Hilbert spaces.  To show the latter I will develop a basis for the nonperturbative Hilbert space of quantum gravity with one asymptotic boundary. I will use this basis to show that the Hilbert space for gravity with two disconnected boundaries factorizes into a product of two copies of the single boundary Hilbert space, from which our main result will follow.

Tidal disruption events — where an unfortunate star is destroyed by a previously quiescent supermassive black hole — offer a unique probe of the low mass end of the supermassive black hole population. Recent observational advances have lead to the discovery of ~100 such events, many of which are comprehensively followed up across the entire electromagnetic spectrum. I will discuss how time-dependent relativistic accretion theory can be used to understand this multi wavelength emission from optical through X-ray energies, and how this theory allows tidal disruption events to act as probes of the massive black hole population. I will present current constraints on the occupation fraction of intermediate mass black holes, and look forward to what can be expected in the LSST era.

Suppose our universe really had a huge cosmological constant.  What would this mean observationally?  For a homogeneous universe the answer is clear, but if the universe is inhomogeneous at the Planck scale the question becomes more subtle.  At the level of initial data, $\Lambda$ can be "hidden" in spacetime foam, rapidly expanding and contracting regions that coexist and give an average expansion near zero.  Classically, such data develop singularities, and we need a quantum description of their evolution.  I describe results from a spherically symmetric midisuperspace model in which the wave function can become "trapped" for long periods in regions in which the average expansion remains small, effectively hiding a large cosmological constant.

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.