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 cosmological constraints from the sample of Type Ia supernovae (SNe Ia) discovered and measured during the full 5 yr of the Dark Energy Survey (DES) SN program. In contrast to most previous cosmological samples, in which SNe are classified based on their spectra, we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each SN being an SN Ia, we find 1635 DES SNe in the redshift range 0.10 < z < 1.13 that pass quality selection criteria sufficient to constrain cosmological parameters. This quintuples the number of high-quality z > 0.5 SNe compared to the previous leading compilation of Pantheon+ and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints, we combine the DES SN data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning 0.025 < z < 0.10. Using SN data alone and including systematic uncertainties, we find Ω_M = 0.352 ± 0.017 in flat ΛCDM. SN data alone now require acceleration (q ₀ < 0 in ΛCDM) with over 5σ confidence. We find ( Ω M , w ) = ( 0.264 − 0.096 + 0.074 , − 0.80 − 0.16 + 0.14 ) in flat wCDM. For flat w ₀ w _a CDM, we find ( Ω M , w 0 , w a ) = ( 0.495 − 0.043 + 0.033 , − 0.36 − 0.30 + 0.36 , − 8.8 − 4.5 + 3.7 ) , consistent with a constant equation of state to within ∼2σ. Including Planck cosmic microwave background, Sloan Digital Sky Survey baryon acoustic oscillation, and DES 3 × 2pt data gives (Ω_M, w) = (0.321 ± 0.007, −0.941 ± 0.026). In all cases, dark energy is consistent with a cosmological constant to within ∼2σ. Systematic errors on cosmological parameters are subdominant compared to statistical errors; these results thus pave the way for future photometrically classified SN analyses.

We present the second public data release of the Dark Energy Survey, DES DR2, based on optical/near-infrared imaging by the Dark Energy Camera mounted on the 4 m Blanco telescope at Cerro Tololo Inter-American Observatory in Chile. DES DR2 consists of reduced single-epoch and coadded images, a source catalog derived from coadded images, and associated data products assembled from 6 yr of DES science operations. This release includes data from the DES wide-area survey covering ∼5000 deg² of the southern Galactic cap in five broad photometric bands, grizY. DES DR2 has a median delivered point-spread function FWHM of g = 1.11″, r = 0.95″, i = 0.88″, z = 0.83″, and Y = 0.″90, photometric uniformity with a standard deviation of < 3 mmag with respect to Gaia DR2 G band, a photometric accuracy of ∼11 mmag, and a median internal astrometric precision of ∼27 mas. The median coadded catalog depth for a 1.″95 diameter aperture at signal-to-noise ratio = 10 is g = 24.7, r = 24.4, i = 23.8, z = 23.1, and Y = 21.7 mag. DES DR2 includes ∼691 million distinct astronomical objects detected in 10,169 coadded image tiles of size 0.534 deg² produced from 76,217 single-epoch images. After a basic quality selection, benchmark galaxy and stellar samples contain 543 million and 145 million objects, respectively. These data are accessible through several interfaces, including interactive image visualization tools, web-based query clients, image cutout servers, and Jupyter notebooks. DES DR2 constitutes the largest photometric data set to date at the achieved depth and photometric precision.

We describe the Dark Energy Survey (DES) photometric data set assembled from the first three years of science operations to support DES Year 3 cosmologic analyses, and provide usage notes aimed at the broad astrophysics community. Y3 GOLD improves on previous releases from DES, Y1 GOLD, and Data Release 1 (DES DR1), presenting an expanded and curated data set that incorporates algorithmic developments in image detrending and processing, photometric calibration, and object classification. Y3 GOLD comprises nearly 5000 deg² of grizY imaging in the south Galactic cap, including nearly 390 million objects, with depth reaching a signal-to-noise ratio ∼10 for extended objects up to i _AB ∼ 23.0, and top-of-the-atmosphere photometric uniformity <3 mmag. Compared to DR1, photometric residuals with respect to Gaia are reduced by 50%, and per-object chromatic corrections are introduced. Y3 GOLD augments DES DR1 with simultaneous fits to multi-epoch photometry for more robust galactic color measurements and corresponding photometric redshift estimates. Y3 GOLD features improved morphological star–galaxy classification with efficiency >98% and purity >99% for galaxies with 19 < i _AB < 22.5. Additionally, it includes per-object quality information, and accompanying maps of the footprint coverage, masked regions, imaging depth, survey conditions, and astrophysical foregrounds that are used to select the cosmologic analysis samples.

We present a new N-body simulation from the Marenostrum Institut de Ciències de l'Espai (MICE) collaboration, the MICE Grand Challenge (MICE-GC), containing about 70 billion dark matter particles in a (3 Gpc h⁻¹)³ comoving volume. Given its large volume and fine spatial resolution, spanning over five orders of magnitude in dynamic range, it allows an accurate modelling of the growth of structure in the universe from the linear through the highly non-linear regime of gravitational clustering. We validate the dark matter simulation outputs using 3D and 2D clustering statistics, and discuss mass-resolution effects in the non-linear regime by comparing to previous simulations and the latest numerical fits. We show that the MICE-GC run allows for a measurement of the BAO feature with per cent level accuracy and compare it to state-of-the-art theoretical models. We also use sub-arcmin resolution pixelized 2D maps of the dark matter counts in the lightcone to make tomographic analyses in real and redshift space. Our analysis shows the simulation reproduces the Kaiser effect on large scales, whereas we find a significant suppression of power on non-linear scales relative to the real space clustering. We complete our validation by presenting an analysis of the three-point correlation function in this and previous MICE simulations, finding further evidence for mass-resolution effects. This is the first of a series of three papers in which we present the MICE-GC simulation, along with a wide and deep mock galaxy catalogue built from it. This mock is made publicly available through a dedicated web portal, http://cosmohub.pic.es.

We present a new parallel implementation of the PINpointing Orbit Crossing-Collapsed HIerarchical Objects (pinocchio) algorithm, a quick tool, based on Lagrangian Perturbation Theory, for the hierarchical build-up of dark matter (DM) haloes in cosmological volumes. To assess its ability to predict halo correlations on large scales, we compare its results with those of an N-body simulation of a 3 h⁻¹ Gpc box sampled with 2048³ particles taken from the mice suite, matching the same seeds for the initial conditions. Thanks to the Fastest Fourier Transforms in the West (FFTW) libraries and to the relatively simple design, the code shows very good scaling properties. The CPU time required by pinocchio is a tiny fraction (∼1/2000) of that required by the mice simulation. Varying some of pinocchio numerical parameters allows one to produce a universal mass function that lies in the range allowed by published fits, although it underestimates the mice mass function of Friends-of-Friends (FoF) haloes in the high-mass tail. We compare the matter–halo and the halo–halo power spectra with those of the mice simulation and find that these two-point statistics are well recovered on large scales. In particular, when catalogues are matched in number density, agreement within 10 per cent is achieved for the halo power spectrum. At scales k > 0.1 h Mpc⁻¹, the inaccuracy of the Zel’dovich approximation in locating halo positions causes an underestimate of the power spectrum that can be modelled as a Gaussian factor with a damping scale of d = 3 h⁻¹ Mpc at z = 0, decreasing at higher redshift. Finally, a remarkable match is obtained for the reduced halo bispectrum, showing a good description of non-linear halo bias. Our results demonstrate the potential of pinocchio as an accurate and flexible tool for generating large ensembles of mock galaxy surveys, with interesting applications for the analysis of large galaxy redshift surveys.