Measuring the neutrino mass from future wide galaxy cluster catalogues
  We present forecast errors on a wide range of cosmological parameters
obtained from a photometric cluster catalogue of a future wide-field
Euclid-like survey. We focus in particular on the total neutrino mass as
constrained by a combination of the galaxy cluster number counts and
correlation function. For the latter we consider only the shape information and
the Baryon Acoustic Oscillations (BAO), while marginalising over the spectral
amplitude and the redshift space distortions. In addition to the cosmological
parameters of the standard LCDM+nu model we also consider a non-vanishing
curvature, and two parameters describing a redshift evolution for the dark
energy equation of state. For completeness, we also marginalise over a set of
"nuisance" parameters, representing the uncertainties on the cluster mass
determination. We find that combining cluster counts with power spectrum
information greatly improves the constraining power of each probe taken
individually, with errors on cosmological parameters being reduced by up to an
order of magnitude. In particular, the best improvements are for the parameters
defining the dynamical evolution of dark energy, where cluster counts break
degeneracies. Moreover, the resulting error on neutrino mass is at the level of
\sigma(M_\nu)\sim 0.9 eV, comparable with that derived from present Ly-alpha
forest measurements and Cosmic Microwave background (CMB) data in the framework
of a non-flat Universe. Further adopting Planck priors and reducing the number
of free parameters to a LCDM+nu cosmology allows to place constraints on the
total neutrino mass of \sigma(M_\nu) \sim 0.08 eV, close to the lower bound
enforced by neutrino oscillation experiments. [abridged]
