We study the characteristics of the galaxy cluster samples expected from the European Space Agencys Euclid satellite and forecast constraints on cosmological parameters describing a variety of cosmological models. The method used in this paper, based
on the Fisher Matrix approach, is the same one used to provide the constraints presented in the Euclid Red Book (Laureijs et al.2011). We describe the analytical approach to compute the selection function of the photometric and spectroscopic cluster surveys. Based on the photometric selection function, we forecast the constraints on a number of cosmological parameter sets corresponding to different extensions of the standard LambdaCDM model. The dynamical evolution of dark energy will be constrained to Delta w_0=0.03 and Delta w_a=0.2 with free curvature Omega_k, resulting in a (w_0,w_a) Figure of Merit (FoM) of 291. Including the Planck CMB covariance matrix improves the constraints to Delta w_0=0.02, Delta w_a=0.07 and a FoM=802. The amplitude of primordial non-Gaussianity, parametrised by f_NL, will be constrained to Delta f_NL ~ 6.6 for the local shape scenario, from Euclid clusters alone. Using only Euclid clusters, the growth factor parameter gamma, which signals deviations from GR, will be constrained to Delta gamma=0.02, and the neutrino density parameter to Delta Omega_ u=0.0013 (or Delta sum m_ u=0.01). We emphasise that knowledge of the observable--mass scaling relation will be crucial to constrain cosmological parameters from a cluster catalogue. The Euclid mission will have a clear advantage in this respect, thanks to its imaging and spectroscopic capabilities that will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies. This information will be further complemented by wide-area multi-wavelength external cluster surveys that will already be available when Euclid flies. [Abridged]
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 i
nformation from cluster number counts and cluster power spectrum. We find that combining cluster data with 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 LCDM+m_nu model the 2 sigma upper limit on total neutrino mass shifts from M_nu < 0.35 eV using cluster data alone to M_nu < 0.031 eV when combined with CMB data. When a non-standard model with N_eff number of neutrino species is considered, we estimate N_eff<3.14 (95% CL), while the bounds on neutrino mass are relaxed to M_nu < 0.040 eV. This accuracy would be sufficient for a 2 sigma detection of neutrino mass even in the minimal normal hierarchy scenario. 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 M_nu is only slightly affected, while there is a larger impact of the order of ~ 15 % and ~ 20% respectively on the 2 sigma error bar of N_eff with respect to the standard case. We also treat the LCDM+m_nu+N_eff case with free nuisance parameters, which parameterize the uncertainties on the cluster mass determination. In this case, the upper bounds on M_nu are relaxed by a factor larger than two, M_nu < 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 [abridged].
