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 Near-Infrared Spectrometer and Photometer (NISP) on board the Euclid satellite provides multiband photometry and R ≳ 450 slitless grism spectroscopy in the 950–2020 nm wavelength range. In this reference article, we illuminate the background of NISP’s functional and calibration requirements, describe the instrument’s integral components, and provide all its key properties. We also sketch the processes needed to understand how NISP operates and is calibrated as well as its technical potentials and limitations. Links to articles providing more details and the technical background are included. The NISP’s 16 HAWAII-2RG (H2RG) detectors with a plate scale of 0″.3 pixel⁻¹ deliver a field of view of 0.57 deg². In photometric mode, NISP reaches a limiting magnitude of ~24.5 AB mag in three photometric exposures of about 100 s in exposure time for point sources and with a S/N of five. For spectroscopy, NISP’s pointsource sensitivity is a signal-to-noise ratio = 3.5 detection of an emission line with flux ~2 × 10⁻¹⁶ erg s⁻¹ cm⁻² integrated over two resolution elements of 13.4 Å in 3 × 560 s grism exposures at 1.6 µm (redshifted Hα). Our calibration includes on-ground and in-flight characterisation and monitoring of the pixel-based detector baseline, dark current, non-linearity, and sensitivity to guarantee a relative photometric accuracy better than 1.5% and a relative spectrophotometry better than 0.7%. The wavelength calibration must be accurate to 5 Å or better. The NISP is the state-of-the-art instrument in the near-infrared for all science beyond small areas available from HST and JWST – and it represents an enormous advance from any existing instrumentation due to its combination of field size and high throughput of telescope and instrument. During Euclid’s six-year survey covering 14 000 deg² of extragalactic sky, NISP will be the backbone in determining distances of more than a billion galaxies. Its near-infrared data will become a rich reference imaging and spectroscopy data set for the coming decades.

This paper presents the specification, design, and development of the Visible Camera (VIS) on the European Space Agency’s Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg² sampled at 0″.1 with an array of 609 Megapixels and a spatial resolution of 0″.18. It will be used to survey approximately 14 000 deg² of extragalactic sky to measure the distortion of galaxies in the redshift range z = 0.1–1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes leveraged by Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and the extent to which this has changed with look-back time can be used to constrain the nature of dark energy and theories of gravity. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, specified to reach m_AB ≥ 24.5 with a signal-to-noise ratio S/N ≥ 10 in a single broad I_E ≃ (r + i + z) band over a six-year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the conception of VIS and describes the instrument design and development, before reporting the prelaunch performance derived from ground calibrations and brief results from the inorbit commissioning. VIS should reach fainter than m_AB = 25 with S/N ≥ 10 for galaxies with a full width at half maximum of 0″. 3 in a 1″.3 diameter aperture over the Wide Survey, and m_AB ≥ 26.4 for a Deep Survey that will cover more than 50 deg². The paper also describes how the instrument works with the Euclid telescope and survey, and with the science data processing, to extract the cosmological information.

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set ofEuclid-like mocks, derived fromN-body simulations. In this first paper of the HOWLS series, we computed the nontomographic (Ω_m,σ₈) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a 4.5 times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses withEuclid. The data used in this analysis are publicly released with the paper.

We present the Flagship galaxy mock, a simulated catalogue of billions of galaxies designed to support the scientific exploitation of the Euclid mission. Euclid is a medium-class mission of the European Space Agency optimised to determine the properties of dark matter and dark energy on the largest scales of the Universe. It probes structure formation over more than 10 billion years primarily from the combination of weak gravitational lensing and galaxy clustering data. The breadth of Euclid’s data will also foster a wide variety of scientific analyses. The Flagship simulation was developed to provide a realistic approximation to the galaxies that will be observed by Euclid and used in its scientific exploitation. We ran a state-of-the-art N-body simulation with four trillion particles, producing a lightcone on the fly. From the dark matter particles, we produced a catalogue of 16 billion haloes in one octant of the sky in the lightcone up to redshift z = 3. We then populated these haloes with mock galaxies using a halo occupation distribution and abundance-matching approach, calibrating the free parameters of the galaxy mock against observed correlations and other basic galaxy properties. Modelled galaxy properties include luminosity and flux in several bands, redshifts, positions and velocities, spectral energy distributions, shapes and sizes, stellar masses, star formation rates, metallicities, emission line fluxes, and lensing properties. We selected a final sample of 3.4 billion galaxies with a magnitude cut of H_E < 26, where we are complete. We have performed a comprehensive set of validation tests to check the similarity to observational data and theoretical models. In particular, our catalogue is able to closely reproduce the main characteristics of the weak lensing and galaxy clustering samples to be used in the mission main cosmological analysis. Moreover, given its depth and completeness, this new galaxy mock also provides the community with a powerful tool for developing a wide range of scientific analyses beyond the Euclid mission.

Context. The cosmological concordance model (ΛCDM) is the current standard model in cosmology thanks to its ability to reproduce the observations. The first observational evidence for this model appeared roughly 20 years ago from the type-Ia supernovae (SNIa) Hubble diagram from two different groups. However, there has been some debate in the literature concerning the statistical treatment of SNIa, and their stature as proof of cosmic acceleration. Aims. In this paper we relax the standard assumption that SNIa intrinsic luminosity is independent of redshift, and examine whether it may have an impact on our cosmological knowledge and more precisely on the accelerated nature of the expansion of the universe. Methods. To maximise the scope of this study, we do not specify a given cosmological model, but we reconstruct the expansion rate of the universe through a cubic spline interpolation fitting the observations of the different cosmological probes: SNIa, baryon acoustic oscillations (BAO), and the high-redshift information from the cosmic microwave background (CMB). Results. We show that when SNIa intrinsic luminosity is not allowed to vary as a function of redshift, cosmic acceleration is definitely proven in a model-independent approach. However, allowing for redshift dependence, a nonaccelerated reconstruction of the expansion rate is able to fit, at the same level of ΛCDM, the combination of SNIa and BAO data, both treating the BAO standard ruler r_d as a free parameter (not entering on the physics governing the BAO), and adding the recently published prior from CMB observations. We further extend the analysis by including the CMB data. In this case we also consider a third way to combine the different probes by explicitly computing r_d from the physics of the early universe, and we show that a nonaccelerated reconstruction is able to nicely fit this combination of low- and high-redshift data. We also check that this reconstruction is compatible with the latest measurements of the growth rate of matter perturbations. We finally show that the value of the Hubble constant (H₀) predicted by this reconstruction is in tension with model-independent measurements. Conclusions. We present a model-independent reconstruction of a nonaccelerated expansion rate of the universe that is able to fit all the main background cosmological probes nicely. However, the predicted value of H₀ is in tension with recent direct measurements. Our analysis points out that a final reliable and consensual value for H₀ is critical to definitively prove cosmic acceleration in a model-independent way.