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.

We present the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. CAMELS is a suite of 4233 cosmological simulations of 25 h − 1 Mpc 3 volume each: 2184 state-of-the-art (magneto)hydrodynamic simulations run with the AREPO and GIZMO codes, employing the same baryonic subgrid physics as the IllustrisTNG and SIMBA simulations, and 2049 N-body simulations. The goal of the CAMELS project is to provide theory predictions for different observables as a function of cosmology and astrophysics, and it is the largest suite of cosmological (magneto)hydrodynamic simulations designed to train machine-learning algorithms. CAMELS contains thousands of different cosmological and astrophysical models by way of varying Ω _m , σ ₈, and four parameters controlling stellar and active galactic nucleus feedback, following the evolution of more than 100 billion particles and fluid elements over a combined volume of ( 400 h − 1 Mpc ) 3 . We describe the simulations in detail and characterize the large range of conditions represented in terms of the matter power spectrum, cosmic star formation rate density, galaxy stellar mass function, halo baryon fractions, and several galaxy scaling relations. We show that the IllustrisTNG and SIMBA suites produce roughly similar distributions of galaxy properties over the full parameter space but significantly different halo baryon fractions and baryonic effects on the matter power spectrum. This emphasizes the need for marginalizing over baryonic effects to extract the maximum amount of information from cosmological surveys. We illustrate the unique potential of CAMELS using several machine-learning applications, including nonlinear interpolation, parameter estimation, symbolic regression, data generation with Generative Adversarial Networks, dimensionality reduction, and anomaly detection.

We present high signal-to-noise galaxy–galaxy lensing measurements of the Baryon Oscillation Spectroscopic Survey constant mass (CMASS) sample using 250 deg² of weak-lensing data from Canada–France–Hawaii Telescope Lensing Survey and Canada–France–Hawaii Telescope Stripe 82 Survey. We compare this signal with predictions from mock catalogues trained to match observables including the stellar mass function and the projected and two-dimensional clustering of CMASS. We show that the clustering of CMASS, together with standard models of the galaxy–halo connection, robustly predicts a lensing signal that is 20–40 per cent larger than observed. Detailed tests show that our results are robust to a variety of systematic effects. Lowering the value of |$S_{\rm 8}=\sigma _{\rm 8} \sqrt{\Omega _{\rm m}/0.3}$| compared to Planck Collaboration XIII reconciles the lensing with clustering. However, given the scale of our measurement (r < 10 h⁻¹ Mpc), other effects may also be at play and need to be taken into consideration. We explore the impact of baryon physics, assembly bias, massive neutrinos and modifications to general relativity on ΔΣ and show that several of these effects may be non-negligible given the precision of our measurement. Disentangling cosmological effects from the details of the galaxy–halo connection, the effect of baryons, and massive neutrinos, is the next challenge facing joint lensing and clustering analyses. This is especially true in the context of large galaxy samples from Baryon Acoustic Oscillation surveys with precise measurements but complex selection functions.