Periodic Reporting for period 1 - CosmoDEC (Cosmological Dark Energy Condensate (CosmoDEC): A unified description of the Dark Universe)
Reporting period: 2021-03-01 to 2023-02-28
Modern physics stands on the shoulders of giants: the General theory of Relativity and the Standard Model of particle physics. The former provides an exceptionally precise description of the gravitational force at vastly different scales, from the solar system to the whole universe. The latter, instead, describes the constituents of matter at the most fundamental level. However, despite representing the state-of-the-art of our understanding of Nature, these models have shortcomings. The emergence of singularities, such as the Big Bang or at the endpoint of the gravitational collapse to form a black hole, clearly signals that General Relativity is no longer applicable and it is necessary to go beyond this model. Furthermore, even when describing the dynamics of the universe at large scales, one is forced to include exotic forms of matter and energy (dubbed dark matter and dark energy, respectively) to reconcile theory and observations. On top of that, while the standard model is an inherently quantum theory, General Relativity is classical and its full quantum-mechanical characterization is unknown. In the corpuscular gravity theory, a new approach to quantum gravity in which the gravitational interaction heals itself by producing marginally bound states of gravitons, the classical notion of spacetime emerges as a collective effect. The objective of the Action was to build upon this idea and show that one can fit gravitational effects at all scales in a unified framework without ingredients beyond the Standard Model. This investigation has led to the formulation of a rigorous formalism describing the emergence of the geometry from a mean-field description of the gravitational interaction. When applied to cosmology, these new tools have confirmed that a modified Newtonian dynamics can emerge at galactic scales as a result of the competition between short- and large-scale (i.e. cosmological) effects in the full quantum state of the system. Furthermore, this new formalism was applied to black hole physics, leading to a natural resolution of important problems afflicting the classical picture of these objects.
The first step toward the implementation of the research program proposed in the Action consisted of a characterization of the quantum state that, in corpuscular gravity, reproduces the emergent classical geometry at macroscopic scales. In order to simplify the analysis, as proposed in the Action, the model was specialized to the case of an expanding universe containing some isolated baryonic matter. This setup models the universe we observe by describing galaxies as localized “impurities”, consisting of ordinary matter placed on top of an expanding geometry. It was soon realized that such a scenario allowed one to explicitly construct the quantum state capable of reproducing the expected classical geometry at macroscopic scales. This state contains an additional contribution, absent in General Relativity, giving rise to an intermediate-scale effect leading to a phenomenology typically attributed to dark matter. In other words, although working in a simplified scenario, our model accounts for dark matter effects without dark matter, thus confirming original hints of the corpuscular approach. Additionally, this model seems to alleviate some of the recently observed “cosmological tensions”. This novel methodology was then generalized and extended to compact objects leading to quantum-mechanical models of black holes without classical singularities or unphysical instabilities. Furthermore, the strong connection between the corpuscular model, effective field theories, and thermodynamics has inspired a novel perspective on the thermodynamic description of modified theories of gravity. More precisely, it was shown how to draw a formal analogy between a wide class of scalar-tensor theories and a famous theory of non-equilibrium thermodynamics. According to this analogy, modifications of the gravitational interaction can be seen as excited states with respect to general relativity, which instead corresponds to an equilibrium state at zero temperature. All the aforementioned results have been published in high-impact scientific journals and presented at international conferences and in university seminars.
The results obtained in this Action have exceeded our expectations. Originally, the idea behind the proposed research was to provide a rough characterization of just the quantum state of a very idealized scenario, such as the case of a single galaxy embedded in an expanding universe, reducing the complexity of the system as much as possible. However, we managed to formulate a brand-new approach, dubbed ``coherent state approach to quantum gravity'', that allowed us to reconstruct the spacetime geometry from a coherent state emerging from a (sort of) mean-field description of the gravitational interaction. This is a major step forward from the corpuscular approach since, for the first time, we have a set of techniques that constitute a solid theoretical basis for the derivation of the corpuscular scaling laws. Furthermore, the emerging quantum geometry for the model of an expanding universe with impurities naturally contains an additional contribution leading to modified dynamics for matter particles at galactic scales, without the need for dark matter. It also softens some of the current cosmological tensions. We managed to extend this approach to black hole geometries, resolving several problems that plague classical black holes. Additionally, the close connection between these corpuscular ideas and thermal physics has opened a window on a new way of understanding the relationship between modified gravity and thermodynamics. Specifically, we proposed a novel thermodynamics of scalar-tensor gravity according to which an abstract ``temperature'' quantifies the departure from general relativity of solutions of a given modified gravity theory, determines whether they are thermally stable, and whether the system relaxes to equilibrium over time. The results of the Action have therefore opened exciting new avenues in the study of quantum gravity and the thermodynamics of gravity, that significantly depart from the mainstream.