Recently, the Planck satellite found a larger and most precise value of the matter energy density, that impacts on the present values of other cosmological parameters such as the Hubble constant, the present cluster abundances and the age of the Univ
erse. The existing tension between Planck determination of these parameters in the frame of the base LambdaCDM model and their direct measurements generated lively discussions and several interpretations. In this paper we quantify this tension by exploring several extensions of the base LambdaCDM model that include the leptonic asymmetry. We set bounds on the radiation content of the Universe and neutrino properties by using the latest cosmological measurements, imposing also self-consistent BBN constraints on the primordial helium abundance. For all cosmological asymmetric models we find the preference of cosmological data for smaller values of active and sterile neutrino masses. This increases the tension between cosmological and short baseline neutrino oscillation data that favor a sterile neutrino with the mass of around 1 eV. For the case of degenerate massive neutrinos, we find that the discrepancies with direct determinations of the Hubble constant, the present cluster abundances and the age of the Universe are alleviated at ~ 1.3 sigma for all leptonic asymmetric models. We also find ~2 sigma statistical evidence of the preference of cosmological data for the normal neutrino hierarchy. This is more evident for the case of cosmological models involving leptonic asymmetry and three massive neutrino species. We conclude that the current cosmological data favor the leptonic asymmetric extension of the base LambdaCDM model and normal neutrino mass hierarchy over the models with additional sterile neutrino species and/or inverted neutrino mass hierarchy.
Distortions of CMB temperature and polarization anisotropy maps caused by gravitational lensing, observable with high angular resolution and sensitivity, can be used to constrain the sterile neutrino mass, offering several advantages against the anal
ysis based on the combination of CMB, LSS and Lyalpha forest power spectra. As the gravitational lensing effect depends on the matter distribution, no assumption on light-to-mass bias is required. In addition, unlike the galaxy clustering and Lyalpha forest power spectra, the projected gravitational potential power spectrum probes a larger range of angular scales, the non-linear corrections being required only at very small scales. Taking into account the changes in the time-temperature relation of the primordial plasma and the modification of the neutrino thermal potential, we compute the projected gravitational potential power spectrum and its correlation with the temperature in the presence of DM sterile neutrino. We show that the cosmological parameters are generally not biased when DM sterile neutrino is included. From this analysis we found a lower limit on DM sterile neutrino mass m_s >2.08 keV at 95% CL, consistent with the lower mass limit obtained from the combined analysis of CMB, SDSS 3D power spectrum and SDSS Lyalpha forest power spectrum ($m_{ u_s}>1.7$ keV). We conclude that although the information that can be obtained from lensing extraction is rather limited due to the high level of the lensing noise of Planck experiment, weak lensing of CMB offers a valuable alternative to constrain the dark matter sterile neutrino mass.
