Abstract: We investigate the non-linear evolution of the relic cosmic neutrino background by running large box-size, high resolution N-body simulations which incorporate cold dark matter (CDM) and neutrinos as independent particle species. Our set of simulations explore the properties of neutrinos in a reference Lambda CDM model with total neutrino masses between 0.05-0.60 eV in cold dark matter haloes of mass 10(11) – 10(15) h(-1) M-circle dot, over a redshift range z = 0 – 2. We compute the halo mass function and show that it is reasonably well fitted by the Sheth-Tormen formula, once the neutrino contribution to the total matter is removed. More importantly, we focus on the CDM and neutrino properties of the density and peculiar velocity fields in the cosmological volume, inside and in the outskirts of virialized haloes. The dynamical state of the neutrino particles depends strongly on their momentum: whereas neutrinos in the low velocity tail behave similarly to CDM particles, neutrinos in the high velocity tail are not affected by the clustering of the underlying CDM component. We find that the neutrino (linear) unperturbed momentum distribution is modified and mass and redshift dependent deviations from the expected Fermi-Dirac distribution are in place both in the cosmological volume and inside haloes. The neutrino density profiles around virialized haloes have been carefully investigated and a simple fitting formula is provided. The neutrino profile, unlike the cold dark matter one, is found to be cored with core size and central density that depend on the neutrino mass, redshift and mass of the halo, for halos of masses larger than similar to 10(13.5) h(-1) M-circle dot. For lower masses the neutrino profile is best fitted by a simple power-law relation in the range probed by the simulations. The results we obtain are numerically converged in terms of neutrino profiles at the 10% level for scales above similar to 200 h(-1) kpc at z = 0, and are stable with respect to box-size and starting redshift of the simulation. Our findings are particularly important in view of upcoming large-scale structure surveys, like Euclid, that are expected to probe the non-linear regime at the percent level with lensing and clustering observations.

Abstract: We compute a new generation of standard solar models (SSMs) that includes recent updates on some important nuclear reaction rates and a more consistent treatment of the equation of state. Models also include a novel and flexible treatment of opacity uncertainties based on opacity kernels, required in. light of recent theoretical and experimental works on radiative opacity. Two large sets of SSMs, each based on a different canonical set of solar abundances with high and low metallicity (Z), are computed to determine model uncertainties and correlations among different observables. We present detailed comparisons of high-and low-Z models against different ensembles of solar observables,. including solar neutrinos, surface helium abundance, depth of the. convective envelope, and sound speed profile. A global comparison, including all observables, yields a p-value of 2.7 sigma for the high-Z model and 4.7 sigma for the low-Z one. When the sound speed differences in the narrow region of 0.65 < r/R-circle dot < 0.70 are excluded from the analysis, results are 0.9 sigma and 3.0 sigma for high-and low-Z models respectively. These results show that. high-Z models agree well with solar data but have a systematic problem right below the bottom of the convective envelope linked to steepness of molecular weight and temperature gradients, and that low-Z models lead to a much more general disagreement with solar data. We also show that, while simple parametrizations of opacity uncertainties can strongly alleviate the solar abundance problem, they are insufficient to substantially improve the agreement of SSMs with helioseismic data beyond that obtained for high-Z models due to the intrinsic correlations of theoretical predictions.