Quantum Gravity

Asymptotically flat spacetimes are invariant under an infinite-dimensional symmetry group comprised of superrotations and supertranslations. These symmetries are spontaneously broken, leading to an infinite degeneracy of gravitational vacua in asymptotically flat spacetimes. Starting from an analysis of four-dimensional asymptotically flat gravity in first order formulation, I will describe how superrotation parametrization modes labelling distinct superrotation vacua are governed by an Alekseev–Shatashvili action on the celestial sphere. I will also comment on a recent construction of a two-dimensional effective action for the Goldstone modes of broken supertranslation invariance.

We introduce the basic elements of tensorial group field theories (TGFTs) for quantum gravity, emphasizing how they encode quantum geometry and their relation with canonical loop quantum gravity and spin foam models. Next, we discuss briefly the issue of continuum limit and how it could be understood in this framework.

In the bulk of the talk, we overview the work on the extraction of an effective cosmological dynamics from TGFTs, inspired by the idea of the universe as a quantum gravity condensate. In this context, we emphasize: the need for appropriately coarse-grained states capturing collective dynamics and the role of relational observables and their construction. We discuss what the theory says (so far) about the fate of the big bang singularity at the beginning of our universe and how it suggests a quantum gravity origin for (phantom) dark energy.

An extension of general relativity (GR) obtained by adding local quadratic terms to the action will be considered. Such theory can be a viable UV completion of GR. The additional terms soften gravity above a certain energy scale and render gravity renormalizable. The presence of 4 derivatives implies via the Ostrogradsky theorem that the classical Hamiltonian is unbounded from below. Nevertheless, I will argue that the relevant solutions are not unstable, but metastable: when the energies are much below a threshold (that is high enough to describe the whole cosmology) runaways are avoided. Remarkably, the chaotic inflation theory of initial conditions ensures that such bound is satisfied and testable implications for the early universe will be discussed. I will also argue that the basic unitarity condition is satisfied when the theory is correctly formulated at the quantum level. Moreover, thanks to the UV softening of gravity, sufficiently light objects must be horizonless and I will discuss explicit analytic examples of horizonless ultracompact objects, which have interesting physical implications.

A fundamental problem of quantum gravity is to understand the quantum evolution of black holes.  While aspects of their evolution are understood asymptotically, a more detailed description of their evolving wavefunction can be provided.  This gives a possible foundation for studying effects that unitarize this evolution, which in turn may provide important clues regarding the quantum nature of gravity.

The issue of whether quantum effects can affect gravity at cosmological distances still lacks a fundamental understanding, but there are indications of a non-trivial gravitational infrared dynamics. This possibility is appealing for building alternatives to the standard cosmological model and explaining the accelerated expansion of the Universe. In this talk I will discuss some large scale modifications of general relativity due to nonlocal terms, which are assumed to arise at the level of quantum effective action. Nonlocality is a general feature of quantum effective actions for theories with massless degrees of freedom and dynamical mass generation is a typical non-perturbative IR effect. Among several models, cosmological requirements select a single structure of the nonlocal term describing a mass for the conformal mode of the metric. The model fits very well cosmological data and has strong signatures in the tensor sector that could be tested in the future by gravitational-wave detections.

The model of Causal Dynamical Triangulations (CDT) is a background-independent and diffeomorphism-invariant approach to quantum gravity,

which provides a lattice regularization of the formal gravitational path integral. The framework does not involve any coordinate system and employs only geometric invariants. For a Universe with toroidal spatial topology, we can introduce coordinates using classical scalar fields with periodic boundary conditions with a jump. The field configurations reveal pictures of cosmic voids and filaments surprisingly similar to the ones observed in the present-day Universe. I will discuss the impact of dynamical matter fields on the geometry of a typical quantum universe in the four-dimensional CDT model and explain several observed phenomena. In particular, a phase transition is triggered by the change of the scalar field jump amplitude. This discovery may have important consequences for quantum universes with non-trivial topology since the phase transition can change the topology to a simply connected one.

In this talk I will discuss how the generators of radial conformal symmetries in Minkowski space-time are related to the generators of time evolution in conformal quantum mechanics. Within this correspondence I will show that in conformal quantum mechanics the state corresponding to the inertial vacuum for a conformally invariant field in Minkowski space-time has the structure of a thermofield double. The latter is built from a bipartite "vacuum state" corresponding to the ground state of the generators of hyperbolic time evolution, which cover only a portion of the time domain. When such generators are the ones of conformal Killing vectors mapping a causal diamond in itself and of dilations, the temperature of the thermofield double reproduces, respectively, the diamond temperature and the Milne temperature perceived by observers whose constant proper time hyper-surfaces define a hyperbolic slicing of the future cone. I will point out how this result indicates that, for conformal invariant fields, the fundamental ingredient for vacuum thermal effects in flat-space time is the non-eternal nature of the lifetime of observers rather than their acceleration.

We are experimentally investigating possible departures from the standard quantum mechanics’  predictions at the Gran Sasso underground laboratory in Italy. In particular, with radiation detectors we are searching signals predicted by the collapse models (spontaneous emission of radiation) which were proposed to solve the “measurement problem” in quantum physics and signals coming from a possible violation of the Pauli Exclusion Principle. 

I shall discuss our recent results published in Nature Physics under the title “Underground test of gravity-related wave function collapse”, where we ruled out the natural parameter-free version of the gravity-related collapse model.  I shall then present more generic results on testing CSL (Continuous Spontaneous Localization) collapse models and discuss future perspectives.

Finally, I shall briefly present the VIP experiment with which we look for possible violations of the Pauli Exclusion Principle by searching for “impossible” atomic transitions and comment the impact of this research in relation to Quantum Gravity models.

 

Asymptotically safe gravity is one of the most conservative approaches to quantum gravity. It relies on the framework of quantum field theory and the Wilsonian renormalization group. Recently, questions and open issues have been discussed both within and outside its community. This week, instead of a seminar, we will have a debate between John Donoghue ("A Critique of the Asymptotic Safety Program", arXiv:1911.02967) and Roberto Percacci ("Critical reflections on asymptotically safe gravity", arXiv:2004.06810), who will critically discuss the status of the field, and highlight its strengths and challenges. 

Across different scales, symmetries shape physical systems: for example, in effective theories in condensed matter, various global symmetries are realized; at higher energy scales, the local symmetries of the Standard Model of particle physics take over. But what is the fate of symmetries at the Planck scale, where quantum gravity fluctuations kick in?

In this talk, I will focus on this question mainly from the perspective of asymptotic safety and will highlight a number of results about the role of symmetries in the interplay of asymptotically safe quantum gravity with matter. I will then mainly focus on particular discrete global symmetries, which have the attractive feature of generating mass-hierarchies without extra fine-tuning, and discuss whether or not these could be realized in quantum-gravity-matter models.

The Hartle-Hawking-Vilenkin state is defined on mini-superspace and is semiclassically related to inflationary theory.  However, the state suffers a few problems connected to the path integral of Euclidean or the Lorentzian measure of metrics.  In this talk, we will explore a way around these issues by working in the (Ashtekar) connection representation, a real Kodama-Chern-Simons state.  We find a generalized "Fourier Transform" that related the Chern-Simons-Kodama state to the Hartle-Hawking state beyond mini-superspace.  We end with some discussion and open ended questions for cosmology and quantum gravity.

I will consider the phase space at null-infinity from the r\rightarrow\infty limit of a quasi-local phase space for a finite box with a boundary that is null. This box will serve as a natural IR regulator. To remove the IR regulator, I will consider a double null foliation together with an adapted Newman--Penrose null tetrad. The limit to null infinity (on phase space) is obtained in the limit where the boundary is sent to infinity. I will introduce various charges and explain the role of the corresponding balance laws. The talk is based on the paper: arXiv:2012.01889.