Quantum Gravity

The classical action, or more generally the path integral, is a convenient framework for extracting the physical consequences of symmetries. In recent years, new symmetries of gravity in asymptotically flat spacetime have been uncovered based on relations to soft theorems governing the S-matrix. I will discuss a program to understand these symmetries using a formulation in which the S-matrix is identified with the action subject to asymptotic boundary conditions. This formulation of the S-matrix is analogous to the GKP/W formulation of the AdS/CFT duality and shares many of its advantages, albeit with new subtleties due to working in asymptotically flat spacetime.

A simple multiverse model explains the late time exponential expansion of our universe without the need of a cosmological constant. Assuming that the local measurement of H_0 is correct, it also give a better fit to data than the standard LCDM model, as well as a z-dependent state parameter w(z) that is not incompatible with the latest DESI data. An (tentative) underlying microscopic theory of the multiverse model, based on W_3 and exceptional Jordan algebras may allow us to calculate the expansion rate of our universe.

In the search for a consistent and renormalizable quantum theory of gravity, a conservative possibility is that gravity admits a field-theoretic description valid up to arbitrarily high energies. This amounts to going beyond the perturbative non-renormalizability of general relativity and it can be achieved following different strategies. One is to abandon Lorentz invariance as a fundamental symmetry to gain power-counting renormalizability, as in Hořava Gravity. In Asymptotically Safe Gravity, ultraviolet completeness instead arises from a non-perturbative renormalization group fixed point, preserving spacetime symmetries. In both cases, the peculiar UV structure of the theory reflects in its low-energy description, with a particular imprint on black hole physics. In this talk, I will explore these two scenarios as UV description of gravity. I will focus both on their high-energy description, reviewing some recent developments, and on the possible low-energy physics stemming from each assumption.

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.

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.