Abstract: The nonequivalence between the metric and Palatini formalisms of f(R) gravity is an intriguing feature of these theories. However, in the recently proposed hybrid metric-Palatini gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed a la Palatini, the “true” gravitational field is described by the interpolation of these two nonequivalent approaches. The theory predicts the existence of a light long-range scalar field, which passes the local constraints and affects the galactic and cosmological dynamics. Thus, the theory opens new possibilities for a unified approach, in the same theoretical framework, to the problems of dark energy and dark matter, without distinguishing a priori matter and geometric sources, but taking their dynamics into account under the same standard.

Abstract: Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metric-Palatini gravitational theory. The latter is constructed by modifying the metric Einstein-Hilbert action with an f(R) term in the Palatini formalism. It was shown that the theory unifies local constraints and the late-time cosmic acceleration, even if the scalar field is very light. In the intermediate galactic scale, we show explicitly that in the hybrid metric-Palatini model the tangential velocity can be explicitly obtained as a function of the scalar field of the equivalent scalar-tensor description. The model predictions are compared model with a small sample of rotation curves of low surface brightness galaxies, respectively, and a good agreement between the theoretical rotation Curves and the observational data is found. The possibility of constraining the form of the scalar field and the parameters of the model by using the stellar velocity dispersions is also analyzed. Furthermore, the Doppler velocity shifts are also obtained in terms of the scalar field. All the physical and geometrical quantities and the numerical parameters in the hybrid metric-Palatini model can be expressed in terms of observable/measurable parameters, such as the tangential velocity, the baryonic mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion velocity, respectively. Therefore, the obtained results open the possibility of testing the hybrid metric-Palatini gravitational models at the galactic or extra-galactic scale by using direct astronomical and astrophysical observations.

Abstract: A plausible explanation for the lightness of neutrino masses is that neutrinos are massless at tree level, with their mass (typically Majorana) being generated radiatively at one or more loops. The new couplings, together with the suppression coming from the loop factors, imply that the new degrees of freedom cannot be too heavy (they are typically at the TeV scale). Therefore, in these models there are no large mass hierarchies and they can be tested using different searches, making their detailed phenomenological study very appealing. In particular, the new particles can be searched for at colliders and generically induce signals in lepton-flavor and lepton-number violating processes (in the case of Majorana neutrinos), which are not independent from reproducing correctly the neutrino masses and mixings. The main focus of the review is on Majorana neutrinos. We order the allowed theory space from three different perspectives: (i) using an effective operator approach to lepton number violation, (ii) by the number of loops at which the Weinberg operator is generated, (iii) within a given loop order, by the possible irreducible topologies. We also discuss in more detail some popular radiative models which involve qualitatively different features, revisiting their most important phenomenological implications. Finally, we list some promising avenues to pursue.