Constraining neutrino properties with a Euclid-like galaxy cluster survey

We perform a forecast analysis on how well a Euclid-like photometric galaxy cluster survey will constrain the total neutrino mass and effective number of neutrino species. We base our analysis on the Monte Carlo Markov Chains technique by combining information from cluster number counts and cluster power spectrum. We find that combining cluster data with Cosmic Microwave Background (CMB) measurements from Planck improves by more than an order of magnitude the constraint on neutrino masses compared to each probe used independently. For the \u39bCDM+m\u3bd model the 2\u3c3 upper limit on total neutrino mass shifts from 11m\u3bd < 0.35 eV using cluster data alone to 11m\u3bd < 0.031 eV when combined with Planck data. When a non-standard scenario with Neff 603.046 number of neutrino species is considered, we estimate an upper limit of Neff < 3.14 (95%CL), while the bounds on neutrino mass are relaxed to 11m\u3bd < 0.040 eV. This accuracy would be sufficient for a 2\u3c3 detection of neutrino mass even in the minimal normal hierarchy scenario ( 11m\u3bd simeq 0.05 eV). In addition to the extended \u39bCDM+m\u3bd+Neff model we also consider scenarios with a constant dark energy equation of state and a non-vanishing curvature. When these models are considered the error on 11m\u3bd is only slightly affected, while there is a larger impact of the order of ~ 15% and ~ 20% respectively on the 2\u3c3 error bar of Neff with respect to the standard case. To assess the effect of an uncertain knowledge of the relation between cluster mass and optical richness, we also treat the \u39bCDM+m\u3bd+Neff case with free nuisance parameters, which parameterize the uncertainties on the cluster mass determination. Adopting the over-conservative assumption of no prior knowledge on the nuisance parameter the loss of information from cluster number counts leads to a large degradation of neutrino constraints. In particular, the upper bounds for 11m\u3bd are relaxed by a factor larger than two, 11m\u3bd < 0.083 eV (95%CL), hence compromising the possibility of detecting the total neutrino mass with good significance. We thus confirm the potential that a large optical/near-IR cluster survey, like that to be carried out by Euclid, could have in constraining neutrino properties, and we stress the importance of a robust measurement of masses, e.g. from weak lensing within the Euclid survey, in order to full exploit the cosmological information carried by such survey