Next generation cosmology: constraints from the Euclid galaxy cluster survey

We study the characteristics of the galaxy cluster samples expected from the European Space Agency's Euclid satellite and forecast constraints on parameters describing a variety of cosmological models. In this paper we use the same method of analysis already adopted in the Euclid Red Book, which is based on the Fisher matrix approach. Based on our analytical estimate of the cluster selection function in the photometric Euclid survey, we forecast the constraints on cosmological parameters corresponding to different extensions of the standard I > cold dark matter model. Using only Euclid clusters, we find that the amplitude of the matter power spectrum will be constrained to Delta sigma(8) = 0.0014 and the mass density parameter to Delta Omega(m) = 0.0011. 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. In combination with Planck cosmic microwave background (CMB) constraints, the amplitude of primordial non-Gaussianity will be constrained to Delta f(NL) a parts per thousand integral 6.6 for the local shape scenario. The growth factor parameter gamma, which signals deviations from general relativity, will be constrained to Delta gamma = 0.02, and the neutrino density parameter to Delta Omega(nu) = 0.0013 (or Delta am(nu) = 0.01). Including the Planck CMB covariance matrix improves dark energy constraints to Delta w(0) = 0.02, Delta w(a) = 0.07, and a FoM = 802. Knowledge of the observable-cluster mass scaling relation is crucial to reach these accuracies. Imaging and spectroscopic capabilities of Euclid will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies, supported by external cluster surveys.