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.
