Massive neutrinos and the Large Scale Structure of the Universe

This thesis deals with the phenomenology of large scale structures in cosmolo- gies with massive neutrinos. Cosmology has the power to constraint the value of neutrino masses down to very high accuracy, but to achieve this target a careful description of the effect neutrinos could induce on cosmological observables is needed. With the help on numerical N-body simulations that include a massive neutrino component we provide results for clustering beyond the linear level of both cold dark matter and neutrinos, comparing the measurements with analytical predictions derived in higher order perturbative approaches and with existing fitting formulae. We also discuss the abundance in mass of tracers of the cold dark matter like halos, identifying the right variable, the variance of the cold dark matter field, that describe the counts measured in the simulations. We highlight the systematics effects introduced by a wrong parametrization of the halo mass function, that can bias the inferred cosmological parameters. We present results for the spatial distribution of halos, focusing on the relation with the underlying cold dark matter distribution. To this end we computed the power spectrum of halos in the simulations, finding that the same variable describing the halo mass function provides a consistent picture of spatial clustering of the halos. The analysis is repeated in redshift space and with higher order correlation functions, the bispectrum in our case, leading to the same conclusions and reinforcing our results.