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 ΛCDM+ν 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 σ(Mν) ∼ 0.9 eV, comparable with that derived from present Lyα 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 ΛCDM+ν cosmology allows to place constraints on the total neutrino mass of σ(Mν) ∼ 0.08 eV, close to the lower bound enforced by neutrino oscillation experiments. Finally, in the optimistic case where uncertainties in the calibration of the mass-observable relation were so small to be neglected, the combination of Planck priors with cluster counts and power spectrum would constrain the total neutrino mass down to σ(Mν) ∼ 0.034 eV, i.e. the minimum neutrino mass predicted by oscillation experiments would be detected in a ΛCDM framework. We thus show that galaxy clusters from future wide galaxy surveys will be an excellent tool for studying cosmology and fundamental physics.