Abstract: Around one-third of the point-like sources in the Fermi-LAT catalogues remain as unidentified sources (unIDs) today. Indeed, these unIDs lack a clear, univocal association with a known astrophysical source. If dark matter (DM) is composed of weakly interacting massive particles (WIMPs), there is the exciting possibility that some of these unIDs may actually be DM sources, emitting gamma-rays from WIMPs annihilation. We propose a new approach to solve the standard, machine learning (ML) binary classification problem of disentangling prospective DM sources (simulated data) from astrophysical sources (observed data) among the unIDs of the 4FGL Fermi-LAT catalogue. We artificially build two systematic features for the DM data which are originally inherent to observed data: the detection significance and the uncertainty on the spectral curvature. We do it by sampling from the observed population of unIDs, assuming that the DM distributions would, if any, follow the latter. We consider different ML models: Logistic Regression, Neural Network (NN), Naive Bayes, and Gaussian Process, out of which the best, in terms of classification accuracy, is the NN, achieving around 93 . 3 per cent +/- 0 . 7 per cent performance. Other ML evaluation parameters, such as the True Ne gativ e and True Positive rates, are discussed in our work. Applying the NN to the unIDs sample, we find that the de generac y between some astrophysical and DM sources can be partially solved within this methodology. None the less, we conclude that there are no DM source candidates among the pool of 4FGL Fermi-LAT unIDs.

Abstract: We analyse the f(R) gravity in the so-called Jordan frame, as implemented to the isotropic Universe dynamics. The goal of the present study is to show that according to recent data analyses of the supernovae Ia Pantheon sample, it is possible to account for an effective redshift dependence of the Hubble constant. This is achieved via the dynamics of a non-minimally coupled scalar field, as it emerges in the f(R) gravity. We face the question both from an analytical and purely numerical point of view, following the same technical paradigm. We arrive to establish that the expected decay of the Hubble constant with the redshift z is ensured by a form of the scalar field potential, which remains essentially constant for z less than or similar to 0.3, independently if this request is made a priori, as in the analytical approach, or obtained a posteriori, when the numerical procedure is addressed. Thus, we demonstrate that an f(R) dark energy model is able to account for an apparent variation of the Hubble constant due to the rescaling of the Einstein constant by the f(R) scalar mode.

Abstract: A non-local action functional for electrodynamics depending on the electric and magnetic fields, instead of potentials, has been proposed in the literature. In this work we elaborate and improve this proposal. We also use this formalism to confront the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov-Bohm effect, two subtle aspects of electrodynamics that we examine in a novel way. We show how the former can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner.