A possible way to capture the effects of quantum gravity in spacetime at a mesoscopic scale, for relatively low energies, is through an energy dependent metric, such that particles with different energies probe different spacetimes. In this context, a clear connection between a geometrical approach and modifications of the special relativistic kinematics has been shown in the last few years. In this work (arXiv:2206.14096), we focus on the geometrical interpretation of the relativistic deformed kinematics present in the framework of doubly special relativity, where a relativity principle is present. In this setting, we study the effects of a momentum dependence of the metric for a uniformly accelerated observer. We show how the local Rindler wedge description gets affected by the proposed observer dependent metric, while the local Rindler causal structure is not, leading to a standard local causal horizon thermodynamic description. For the proposed modified metric, we can reproduce the derivation of Einstein’s equations as the equations of state for the thermal Rindler wedge. The conservation of the Einstein tensor leads to the same privileged momentum basis obtained in other works of some of the present authors, so supporting its relevance.

In this paper (arXiv:2206.12717) we consider an N-dimensional multiparametric generalization of the classical Zernike system. We prove that it always provides a superintegrable system by obtaining the corresponding constants of the motion explicitly, which turn out to be of higher-order in the momenta. Such generic results are not only applied to the Euclidean plane, but also to the sphere and the hyperbolic plane. In the latter curved spaces, the Hamiltonian is expressed in geodesic polar coordinates showing that such a new superintegrable Hamiltonian can be regarded as a superposition of the isotropic 1:1 curved (Higgs) oscillator with even-order anharmonic curved oscillators plus another superposition of higher-order momentum-dependent potentials. Furthermore, the Racah algebra determined by the constants of the motion is also studied, giving rise to a (2N−1)th-order polynomial algebra. As a byproduct, the Hamiltonian is interpreted as a family of superintegrable perturbations of the classical Zernike system. Finally, it is shown that this new Hamiltonian (and so the Zernike system as well) is endowed with a Poisson 𝔰𝔩(2,ℝ)-coalgebra symmetry which would allow for further possible generalizations that are also discussed.

Graphene nanostructures have attracted a lot of attention in recent years due to their unconventional properties. In this paper we have employed Density Functional Theory to study the mechanical and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For each case, we have analysed the behaviour of curvature energy and of quantum regeneration times (classical and revival) as the spherical sector radius changes. Revival time presents in one case a divergence usually associated with a phase transition, probably caused by the pseudomagnetic field created by the curvature. This could be the first case of a phase transition in graphene nanostructures without the presence of external electric or magnetic fields.

In these lecture notes (arXiv:2202.09170) it is reviewed how multi-messenger astronomy provides for the observation of the same astronomical event with different kind of telescopes at the same time: optical observations, X-rays, gamma-ray bursts, neutrinos and, most recently, gravitational waves are just few examples of the several points of view from which an astronomical event can be observed and analyzed. Cosmic rays play an important role in multi-messenger astronomy and, for this reason, it is important to deepen the study of their sources and to understand the mechanisms behind their acceleration in astronomical environments.

In this work (arXiv: 2203.12286) we discuss the deformed relativistic wave equations, namely the Klein–Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein–Gordon case.

In this new paper (arXiv:2202.11767), the noncommutative space of light-like worldlines that is covariant under the light-like (or null-plane) κ-deformation of the (3+1) Poincaré group is fully constructed as the quantization of the corresponding Poisson homogeneous space of null geodesics. This new noncommutative space of geodesics is five-dimensional, and turns out to be defined as a quadratic algebra that can be mapped to a non-central extension of the direct sum of two Heisenberg-Weyl algebras whose noncommutative parameter is just the Planck scale parameter κ−1. Moreover, it is shown that the usual time-like κ-deformation of the Poincaré group does not allow the construction of the Poisson homogeneous space of light-like worldlines. Therefore, the most natural choice in order to model the propagation of massless particles on a quantum Minkowski spacetime seems to be provided by the light-like κ-deformation.

In this article published in the February 2022 number of the New Scientist, the novel structure of space-time arising from a quantum perspective is presented from different viewpoints. Among them, the idea that by exchanging quantum information, observers can create a shared reality, even if it isn’t there from the start, is presented.

The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review (arXiv:2111.05659) is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.

A video-abstract of this review is available here.