  Cosmological neutrinos strongly affect the evolution of the largest
structures in the Universe, i.e. galaxies and galaxy clusters. We use large
box-size full hydrodynamic simulations to investigate the non-linear effects
that massive neutrinos have on the spatial properties of cold dark matter (CDM)
haloes. We quantify the difference with respect to the concordance LambdaCDM
model of the halo mass function and of the halo two-point correlation function.
We model the redshift-space distortions and compute the errors on the linear
distortion parameter beta introduced if cosmological neutrinos are assumed to
be massless. We find that, if not taken correctly into account and depending on
the total neutrino mass, these effects could lead to a potentially fake
signature of modified gravity. Future nearly all-sky spectroscopic galaxy
surveys will be able to constrain the neutrino mass if it is larger than 0.6
eV, using beta measurements alone and independently of the value of the matter
power spectrum normalisation. In combination with other cosmological probes,
this will strengthen neutrino mass constraints and help breaking parameter
degeneracies.
