**BOLOGNA**

- We investigate the Ultraviolet completion of quantum gravity, interacting with other fields using the Functional Renormalization Group technique in the framework of the Asymptotic Safety approach. We develop different version of the Renormalization group formalism and its applications to the quantum field theory in curved spacetimes.
- The new approaches to the classical and quantum physics of black holes are under study. Between these approaches are Bootstrapped Newtonian Gravity and Horizon Quantum Mechanics. We will hence continue to develop the HQM and BNG in order to study quantum processes in the gravitational collapse of compact (astrophysical) objects that could possibly be seen by means of gravitational wave detectors and other observations.
- We shall continue to study the physics both of the very early and late-time universe. The very early stages may be greatly influenced by Quantum Gravity effects and are then closely connected with the development of quantum cosmology. We shall apply the cosmological Wheeler-DeWitt equation to the structure of the CMBR and generalise our formalism and results to MGT. General aspects of the QFT of constrained systems will be analysed as well.
- The problem of singularity in gravitational theories is studied in both cosmological and black holes contexts.

**CATANIA**

We plan to investigate on the expected connection, though not clearly understood, between the continuum limit realized in the Asymptotic Safety (AS) scenario and Horava-Lifshitz gravity. In fact, in the first case there are strong indications that the UV region of the theory is characterized by a non-gaussian fixed point for which the (negative) anomalous dimension of the (background) graviton is dynamically generated through a non-pertubative mechanism, while in the case of the HL gravity, the anomalous scaling is explicitly realized in the bare lagrangian. In particular, starting from the studies (Zappala' 2018) that we recently carried out on the peculiar properties of the Lifshitz points, we intend to analyze in detail the UV and IR structure of of higher derivative theories that possess this kind of fixed points, either isotropic or anisotropic, in order to achieve a clearer picture of their phase diagram. In addition we hope to achieve a better understanding of the nature of possible unphysical modes such as tachyons or negative norm states, etc, in relation with the structure of the vacuum as this latter can be non-trivial in these theories.

**MILANO**

- De Sitter and Anti-de Sitter: we shall continue our studies of de Sitter anti-de Sitter and the RG, the perturbation theory in the de Sitter spacetime and the flat limit. We have developed new techniques to compute loop diagrams on the de Sitter space which look very promising, also to the aim of computing higher quantum correction to the effective action of the SM at inflation. We believe that interesting facts that can be learned in the flat space limit concerning the structure of Feynman diagrams in Minkowski space.
- Hawking radiation: we aim to construct exactly solvable classical and quantum dispersive models with strong non-linear time-dispersion laws. Such models should provide a much better treatment of the wave equations compared to standard perturbation theory to be applied to the experiments performed in Como and Edinburgh.
- String field theory and super-geometry: we shall continue the investigation of bosonic string field theory studying possible supersymmetric extensions to tackle the tachyon states issue and study its finite temperature representation and the related Hagedorn phenomenon. The development of a consistent algebro-geometric formulation of perturbative superstring theory will be carried on.
- The cosmological constant problem: different theoretical approaches will be studied ranging from postulating a different coupling between the vacuum energy of QFT and gravity, considering new form of highly non-linear interaction in the matter sector or suggesting a new, highly anisotropic and inhomogeneous, description of the quantum vacuum “fluid”.
- Non-local theories of gravity: such theories are described by non-local operators and thus generate long range effects which can also explain the observed cosmic acceleration. However, their consistency with Solar System observations must be checked. Recent results indicate that small scale effects in such theories can be screened and they can pass lunar laser ranging tests.
- Inflationary cosmology: we shall continue our study of the quantum effects during inflation and their possible observable effects..

**PISA**

- Formal developments of AS and universality: The AS approach to gravity is generally studied with scheme-dependent methods, which are enough to prove the existence of an UV completion, but cannot be used to draw scheme-independent conclusions. We developed a generalization of dimensional regularization that allows to discuss the UV completion in a universal fashion, although perturbatively, leading for the first time to the “true” on-shell spectrum of AS gravity. We then evinced the existence of a pseudo-observable “true quantum metric”, which we will use for to the construction of “true” observables defined as composite operators.
- MAG in the UV and Weyl symmetry: In general, UV completions of field theories (including gravity) are expected to be scale or even conformal-invariant. Since MAG theories could potentially be completions of metric’s gravity, we have discussed the interesting effects that Weyl symmetry has on their degrees of freedom: a gauge potential for local scale symmetry can be interpreted either as torsion or as disformation of the metric’s Christoffel connection. Such gauge potential can be seen as a minimal modification of the SM, which has potentially important effects. Using our findings, we are constructing viable complete theories within the MAG framework, i.e. theories that avoid negative-norm states and are stable at high energies.

**TRENTO**

- Scale invariant gravity: Cosmological models based on scale-invariance have attract-ed much attention. Generally, these are non-minimally coupled scalar-tensor theories with quadratic curvature terms in the action. These models spontaneously break scale-invariance, both dynamically and quantum-mechanically, and generate an effective mass scale. When applied to inflation, they reproduce the observed spectral indices and our aim is now to verify they robustness against observations in more detail by studying NG and the possibility to generate PBHs. We shall explore possible extensions of these models in two directions: a) including other scale-invariant contributions that might be present during inflation (abelian or non-abelian fields, more scalar fields, other quadratic curvature terms), b) including spatial curvature and then studying bouncing cosmologi-cal solutions. Finally, in this context, we shall search for new BH solutions which can possibly alleviate the problem of singularities.
- Cosmology: this research line is focused on probing fundamental physics by looking for imprints on cosmological, astrophysical, and terrestrial data, exploiting the synergy between different types of probes, and constructing viable data-driven theoretical mod-els of our Universe. We shall study neutrino cosmology, the viability of theoretical models with non-standard dark sector physics given their ability to solve some cosmological tensions. We will use BH shadows to test exotic new physics and study aspects of fun-damental physics leading to violations of the no-hair theorem. We will assess the possi-bility of directly detecting DE quanta in existing terrestrial DM direct detection experiments.

**TRIESTE**

MAG and HDG: HDG theory, with terms quadratic in the Riemann and Ricci tensors, have been reconsidered recently as an acceptable theory of QG since new concrete proposals tackling the issue of unitarity have been developed. MAG theories, where the connection is treated as an independent variable, are of special interest, in particular when the action is quadratic in the curvature tensor, because their structure is very similar to that of gauge theories. Given a metric, one can write an arbitrary connection as the sum of the Levi-Civita connection plus a massive tensor field. It is interesting to investigate when its mass is much lower than its natural, Planck mass, value and if there exist classes of actions that have acceptable propagators and are perturbatively renormalizable. The general action for such theories still depends on many parameters but a study limited to certain subclasses of theories, with special symmetries and fewer parameters could also be relevant. Cosmology and BHs physics: In the past, we emphasized the difficulties in the description of tunneling with creation of BHs/wormholes adopting QFT methods extended to curved backgrounds. We plan to study how to avoid such technical difficulties, in particular arising in the application of the WKB approximation.

Symmetry restoration has been studied in connection with the Unruh effect, and considers the possibility that a uniformly accelerated observer, who sees the vacuum of an inertial observer as a thermal bath, might also see a different phase of an underlying symmetry. The literature on the subject presents contradictory conclusions, and we would like to clarify this issue. Additionally, we would like to extend the analysis to a genuinely curved background such as the inflationary background, thus relating this latter problem to the ideas related to tunneling and discussed above.

We shall continue the study of asymptotic symmetries, to improve our understanding of boundary degrees of freedom, the associated boundary conditions and symmetry algebras. We plan to expand our recent investigations of the interplay between symmetry and Einstein’s equations at asymptotic null infinity.

Finally, the group will continue to develop computational tools, in connection with the above research, and with applications to the description of astrophysical systems.