Luciano Gabbanelli

Analytic compartmental models are currently used in mathematical epidemiology to forecast the COVID-19 pandemic evolution and explore the impact of mitigation strategies. In general, such models treat the population as a single entity, losing the social, cultural and economical specificities. We present a network model that uses socio-demographic datasets with the highest available granularity to predict the spread of COVID-19 in the province of Barcelona. The model is flexible enough to incorporate the effect of containment policies, such as lockdowns or the use of protective masks, and can be easily adapted to future epidemics. We follow a stochastic approach that combines a compartmental model with detailed individual microdata from the population census, including social determinants and age-dependent strata, and time-dependent mobility information. We show that our model reproduces the dynamical features of the disease across two waves and demonstrates its capability to become a powerful tool for simulating epidemic events.

In this review we focus on the main cosmological implications of the Group Field Theory approach, according to which an effective continuum macroscopic dynamics can be extracted from the underlying formalism for quantum gravity. Within this picture what counts is the collective behaviour of a large number of quanta of geometry. The resulting state is a condensate-like structure made of "pre-geometric" excitations of the Group Field Theory field over a no-space vacuum. Starting from the kinematics and dynamics, we offer an overview of the way in which Group Field Theory condensate cosmology treats solutions for the homogeneous and isotropic universe. These solutions including a bounce, share with other quantum cosmological approaches the resolution of the singularity characterizing general relativity. Contrary to what is usually done in quantum cosmology, in GFT cosmology no preliminary symmetry reduction is needed for this purpose. We conclude with a discussion of the limits and future perspectives of the Group Field Theory approach.

Pulsar timing arrays have yet to convincingly observe gravitational waves. Some time ago it was pointed out by one of the authors that a dramatic enhancement of the signal would take place for particular values of the angle subtended by the source and the observed pulsar. This enhancement is due to the fact that waves propagate in a Friedmann–Lemaitre–Robertson–Walker metric where, contrary to some wide-spread belief, a simple harmonic function with a red-shifted frequency is not a solution of the equation of motion. At the first non-trivial order, proper solutions have an effective wave number that differs from the frequency. This leads to some interesting effects in pulsar timing arrays whose most visible manifestation is the enhancement of the signal that, all other parameters kept fixed, is related in a simple manner to the value of H ₀ . In this work, we rederive in an alternative way the main results, extend the formalism to a more realistic setting where all components in the cosmological budget are included, investigate in detail the dependence of the signal on the various parameters involved and propose an observational set-up to hopefully detect this very relevant effect.

We employ the minimal geometric deformation approach to gravitational decoupling (MGD- decoupling) in order to build an exact anisotropic version of the Schwarzschild interior solution in a space-time with cosmological constant. Contrary to the well-known Schwarzschild interior, the matter density in the new solution is not uniform and possesses subluminal sound speed. It therefore satisfies all standard physical requirements for a candidate astrophysical object.

We study here how the presence of non-zero matter density and a cosmological constant could affect the observation of gravitational waves in pulsar timing arrays. Conventionally, the effect of matter and cosmological constant is included by considering the redshift in frequency due to the expansion. However, there is an additional interesting effect due to the change of coordinates from the ones describing the geometry of the region where waves are produced to the ones used to measure the pulsar timing residuals. This change of coordinates is unavoidable as the strong gravitational field in a black hole merger distorts clocks and rules. Harmonic waves produced in such a merger become anharmonic when detected by a cosmological observer. The effect is tiny but appears to be nevertheless observable for the type of gravitational waves to which pulsar timing arrays are sensitive and for the favoured values of the cosmological parameters.

We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose–Einstein condensate of gravitons. In order to do so we extend the Einstein–Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross–Pitaevskii equation describing a graviton Bose–Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose–Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.

In the present work, a hidden scenario which cast a long-lived superheavy particle [Formula: see text] and simultaneously an extremely light particle [Formula: see text] with mass [Formula: see text] eV is presented. The potential energy [Formula: see text] of the particle [Formula: see text] models the vacuum energy density of the universe [Formula: see text]. On the other hand, the [Formula: see text] particle may act as superheavy dark matter at present times and the products of its decay may be observed in high energy cosmic ray events. The hidden sector proposed here include light fermions with masses near the neutrino mass [Formula: see text] eV and superheavy ones with masses of the order of the GUT scale, interacting through a hidden SU(2)_L interaction which also affects the ordinary sector. The construction of such combined scenario is nontrivial since the presence of light particles may spoil the stability of the heavy particle [Formula: see text]. However, double Higgs mechanisms may be helpful for overcoming this problem. In this context, the stability of the superheavy particle [Formula: see text] is ensured due to chiral symmetry arguments elaborated in the text.