The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

The abundance of galaxy clusters can constrain both the geometry and growth of structure in our Universe. However, this probe could be significantly complicated by recent claims of non-universality–non-trivial dependences with respect to the cosmological model and redshift. In this work, we analyse the dependence of the mass function on the way haloes are identified and establish if this can cause departures from universality. In order to explore this dependence, we use a set of different N-body cosmological simulations (Le SBARBINE simulations), with the latest cosmological parameters from the Planck collaboration; this first suite of simulations is followed by a lower resolution set, carried out with different cosmological parameters. We identify dark matter haloes using a spherical overdensity algorithm with varying overdensity thresholds (virial, 2000, 1000, 500, 200 ρ_c and 200 ρ_b) at all redshifts. We notice that, when expressed in terms of the rescaled variable ν, the mass function for virial haloes is a nearly universal as a function of redshift and cosmology, while this is clearly not the case for the other overdensities we considered. We provide fitting functions for the halo mass function parameters as a function of overdensity, that allow us to predict, to within a few per cent accuracy, the halo mass function for a wide range of halo definitions, redshifts and cosmological models. We then show how the departures from universality associated with other halo definitions can be derived by combining the universality of the virial definition with the expected shape of the density profile of haloes.

Gravitational lensing by clusters of galaxies offers a powerful probe of their structure and mass distribution. Several research groups have developed techniques independently to achieve this goal. While these methods have all provided remarkably high precision mass maps, particularly with exquisite imaging data from the Hubble Space Telescope (HST), the reconstructions themselves have never been directly compared. In this paper, we present for the first time a detailed comparison of methodologies for fidelity, accuracy and precision. For this collaborative exercise, the lens modeling community was provided simulated cluster images that mimic the depth and resolution of the ongoing HST Frontier Fields. The results of the submitted reconstructions with the un-blinded true mass profile of these two clusters are presented here. Parametric, free-form and hybrid techniques have been deployed by the participating groups and we detail the strengths and trade-offs in accuracy and systematics that arise for each methodology. We note in conclusion that several properties of the lensing clusters are recovered equally well by most of the lensing techniques compared in this study. For example, the reconstruction of azimuthally averaged density and mass profiles by both parametric and free-form methods match the input models at the level of ∼10%. Parametric techniques are generally better at recovering the two-dimensional maps of the convergence and of the magnification. For the best performing algorithms, the accuracy in the magnification estimate is ∼10% at μ_true = 3 and it degrades to ∼30% at μ_true ∼ 10.

Galaxy clusters contain more small-scale gravitational lenses than expected from cosmological simulations.

We present a simple, semi-analytical model to compute the mass functions of dark matter subhaloes. The masses of subhaloes at their time of accretion