We present a new approach to the mathematical objects of General Relativity in terms of which a generic f (R)-gravity theory gravitation is written in a first-order (à la Palatini) formalism, and introduce the concept of Dark Metric which could bypass the emergence of disturbing concepts as Dark Energy and Dark Matter. These issues are related to the fact that General Relativity could not be the definitive theory of Gravitation due to several shortcomings that come out both from theoretical and experimental viewpoints. At large scales, the attempts to match it with the recent observational data lead to invoke Dark Energy and Dark Matter as the bulk components of the cosmic fluid. Since no final evidence, at fundamental level, exists for such ingredients, it could be useful to reconsider the gravitational sector in order to see if suitable extensions of General Relativity could solve the shortcomings present at infrared scales.

We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in [1] does not trivially reduce to f (R) models. It will also produce an example of theory that on-shell endowes spacetime with a non-trivial Weyl geometry where the connection is not induced by the metric structure (though it is compatible with it in the sense of Ehlers-Pirani-Schild; see [2]).

Migration from low- and middle-income countries to high-income countries increasingly determines the severity of tuberculosis (TB) cases in the adopted country. Socially marginalized groups, about whom little is known, may account for a reservoir of TB among the immigrant populations. We investigated the rates of and risk factors for Mycobacterium tuberculosis transmission, infection, and disease in a cohort of 27,358 socially marginalized immigrants who were systematically screened (1991–2010) in an area of Italy with low TB incidence. Overall TB and latent TB infection prevalence and annual tuberculin skin testing conversion rates (i.e., incidence of new infection) were 2.7%, 34.6%, and 1.7%, respectively. Prevalence of both TB and latent TB infection and incidence of infection increased as a function of the estimated TB incidence in the immigrants’ countries of origin. Annual infection incidence decreased with time elapsed since immigration. These findings have implications for control policy and immigrant screening in countries with a low prevalence of TB.

Abstract. General Relativity is not the definitive theory of Gravitation due to several shortcomings which are coming out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological scales) the attempts to match it with the today observational data lead to invoke Dark Energy and Dark Matter as the bulk components of the cosmic fluid. Since no final evidence, at fundamental level, exists for such ingredients, it is clear that General Relativity presents shortcomings at infrared scales. On the other hand, the attempts to formulate theories more general than the Einstein one give rise to mathematical difficulties that need workarounds which, in turn, generate problems from the interpretative viewpoint. We present here a completely new approach to the mathematical objects in terms of which a theory of Gravitation may be written in a first-order (à la Palatini) formalism, and introduce the concept of Dark Metric which could completely bypass the introduction of disturbing concepts as Dark Energy and Dark Matter.

Abstract:We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural Theories" that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.). It is discussed how the use of Poincaré-Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as "generators of Noether symmetries", energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-called ADM laws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation "à la Palatini" and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero-Immirzi connections).