Abstract: New measurements of the cosmic microwave background (CMB) by the Planck mission have greatly increased our knowledge about the universe. Dark radiation, a weakly interacting component of radiation, is one of the important ingredients in our cosmological model which is testable by Planck and other observational probes. At the moment, the possible existence of dark radiation is an unsolved question. For instance, the discrepancy between the value of the Hubble constant, H-0, inferred from the Planck data and local measurements of H-0 can to some extent be alleviated by enlarging the minimal ACDM model to include additional relativistic degrees of freedom. From a fundamental physics point of view, dark radiation is no less interesting. Indeed, it could well be one of the most accessible windows to physics beyond the standard model, for example, sterile neutrinos. Here, we review the most recent cosmological results including a complete investigation of the dark radiation sector in order to provide an overview of models that are still compatible with new cosmological observations. Furthermore, we update the cosmological constraints on neutrino physics and dark radiation properties focusing on tensions between data sets and degeneracies among parameters that can degrade our information or mimic the existence of extra species.

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.