Accurate knowledge of galaxy redshift distributions is crucial in the inference of cosmological parameters from large-scale structure data. We explore the potential for enhanced self-calibration of photometric galaxy redshift distributions, n(z), through the joint analysis of up to six two-point functions. Our 3 × 2 pt configuration comprises photometric shear, spectroscopic galaxy clustering, and spectroscopic-photometric galaxy-galaxy lensing (GGL). We expand this to include spectroscopic-photometric cross-clustering, photometric GGL, and photometric auto-clustering, using the photometric shear sample as an additional density tracer. We performed simulated likelihood forecasts of the cosmological and nuisance parameter constraints for stage-III- and stage-IV-like surveys. For the stage-III-like survey, we employed realistic redshift distributions with perturbations across the full shape of the n(z), and distinguished between ‘coherent’ shifting of the bulk distribution in one direction, versus more internal scattering and full-shape n(z) errors. For perfectly known n(z), a 6 × 2 pt analysis gains ∼40% in figure of merit (FoM) on the S₈ ≡ σ₈√Ω_m/0.3 and Ω_m plane relative to the 3 × 2 pt analysis. If untreated, coherent and incoherent redshift errors lead to inaccurate inferences of S₈ and Ω_m, respectively, and contaminate inferences of the amplitude of intrinsic galaxy alignments. Employing bin-wise scalar shifts, δz_i, in the tomographic mean redshifts reduces cosmological parameter biases, with a 6 × 2 pt analysis constraining the δz_i parameters with 2 − 4 times the precision of a photometric 3^ph × 2 pt analysis. For the stage-IV-like survey, a 6 × 2 pt analysis doubles the FoM (σ₈–Ω_m) compared to the 3 × 2 pt or 3^ph × 2 pt analyses, and is only 8% less constraining than if the n(z) were perfectly known. A Gaussian mixture model for the n(z) is able to reduce mean-redshift errors whilst preserving the n(z) shape, and thereby yields the most accurate and precise cosmological constraints for any given N × 2 pt configuration in the presence of n(z) biases.

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.

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 000 . 1 with an array of 609 Megapixels and a spatial resolution of 000 . 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 mAB ≥ 24.5 with a signal-to-noise ratio S/N ≥ 10 in a single broad IE ≃ (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 in-orbit commissioning. VIS should reach fainter than mAB = 25 with S/N ≥ 10 for galaxies with a full width at half maximum of 000 . 3 in a 100 . 3 diameter aperture over the Wide Survey, and mAB ≥ 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.

The Near-Infrared Spectrometer and Photometer (NISP) on board the Euclid satellite provides multiband photometry and R â ³ 450 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 03.3 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 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 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.

The near-infrared calibration unit (NI-CU) on board Euclid’s Near-Infrared Spectrometer and Photometer (NISP) is the first astronomical calibration lamp based on light-emitting diodes (LEDs) to be operated in space. Euclid is a mission in ESA’s Cosmic Vision 2015–2025 framework to explore the dark universe and provide a next-level characterisation of the nature of gravitation, dark matter, and dark energy. Calibrating photometric and spectrometric measurements of galaxies to better than 1.5% accuracy in a survey homogeneously mapping ∼14 000 deg2 of extragalactic sky requires a very detailed characterisation of near-infrared (NIR) detector properties as well as constant monitoring of them in flight. To cover two of the main contributions – relative pixel-to-pixel sensitivity and non-linearity characteristics – and to support other calibration activities, NI-CU was designed to provide spatially approximately homogeneous (<12% variations) and temporally stable illumination (0.1–0.2% over 1200 s) over the NISP detector plane with minimal power consumption and energy dissipation. NI-CU covers the spectral range ∼[900,1900] nm – at cryo-operating temperature – at five fixed independent wavelengths to capture wavelength-dependent behaviour of the detectors, with fluence over a dynamic range of ≳100 from ∼15 ph s−1 pixel−1 to >1500 ph s−1 pixel−1. For this functionality, NI-CU is based on LEDs. We describe the rationale behind the decision and design process, the challenges in sourcing the right LEDs, and the qualification process and lessons learned. We also provide a description of the completed NI-CU, its capabilities, and performance as well as its limits. NI-CU has been integrated into NISP and the Euclid satellite, and since Euclid’s launch in July 2023, it has started supporting survey operations.

Context. The Euclid mission of the European Space Agency will deliver weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and extensions thereof. Aims. We present forecasts from the combination of the Euclid photometric galaxy surveys (weak lensing, galaxy clustering, and their cross-correlations) and its spectroscopic redshift survey with respect to their sensitivity to cosmological parameters. We include the summed neutrino mass, Σmν, and the effective number of relativistic species, Neff, in the standard Λ CDM scenario and in the dynamical dark energy (w0waCDM) scenario. Methods. We compared the accuracy of different algorithms predicting the non-linear matter power spectrum for such models. We then validated several pipelines for Fisher matrix and Markov chain Monte Carlo (MCMC) forecasts, using different theory codes, algorithms for numerical derivatives, and assumptions on the non-linear cut-off scale. Results. The Euclid primary probes alone will reach a sensitivity of σ (Σmν = 60 meV) = 56 meV in the Λ CDM+Σmν model, whereas the combination with cosmic microwave background (CMB) data from Planck is expected to achieve σ (Σmν) = 23 meV, offering evidence of a non-zero neutrino mass to at least the 2.6 σ level. This could be pushed to a 4 σ detection if future CMB data from LiteBIRD and CMB Stage-IV were included. In combination with Planck, Euclid will also deliver tight constraints on Δ Neff < 0.144 (95%CL) in the Λ CDM+Σmν+Neff model or even Δ Neff < 0.063 when future CMB data are included. When floating the dark energy parameters, we find that the sensitivity to Neff remains stable, but for Σmν, it gets degraded by up to a factor of 2, at most. Conclusions. This work illustrates the complementarity among the Euclid spectroscopic and photometric surveys and among Euclid and CMB constraints. Euclid will offer great potential in measuring the neutrino mass and excluding well-motivated scenarios with additional relativistic particles.

In this paper we present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute the exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases ('shot noise') in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid's first data release.

Galaxy proto-clusters are receiving increased interest since most of the processes shaping the structure of clusters of galaxies and their galaxy population happen at the early stages of their formation. The Euclid Survey will provide a unique opportunity to discover a large number of proto-clusters over a large fraction of the sky (14 500 deg2). In this paper, we explore the expected observational properties of proto-clusters in the Euclid Wide Survey by means of theoretical models and simulations. We provide an overview of the predicted proto-cluster extent, galaxy density profiles, mass-richness relations, abundance, and sky-filling as a function of redshift. Useful analytical approximations for the functions of these properties are provided. The focus is on the redshift range z = 1.5-4. In particular we discuss the density contrast with which proto-clusters can be observed against the background in the galaxy distribution if photometric galaxy redshifts are used as supplied by the ESA Euclid mission together with the ground-based photometric surveys. We show that the obtainable detection significance is sufficient to find large numbers of interesting proto-cluster candidates. For quantitative studies, additional spectroscopic follow-up is required to confirm the proto-clusters and establish their richness.

The Euclid mission of the European Space Agency will provide weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and its extensions, with an opportunity to test the properties of dark matter beyond the minimal cold dark matter paradigm. We present forecasts from the combination of the Euclid weak lensing and photometric galaxy clustering data on the parameters describing four interesting and representative non-minimal dark matter models: a mixture of cold and warm dark matter relics; unstable dark matter decaying either into massless or massive relics; and dark matter undergoing feeble interactions with relativistic relics. We modelled these scenarios at the level of the non-linear matter power spectrum using emulators trained on dedicated N-body simulations. We used a mock Euclid likelihood and Monte Carlo Markov chains to fit mock data and infer error bars on dark matter parameters marginalised over other parameters. We find that the Euclid photometric probe (alone or in combination with cosmic microwave background data from the Planck satellite) will be sensitive to the effect of each of the four dark matter models considered here. The improvement will be particularly spectacular for decaying and interacting dark matter models. With Euclid, the bounds on some dark matter parameters can improve by up to two orders of magnitude compared to current limits. We discuss the dependence of predicted uncertainties on different assumptions: the inclusion of photometric galaxy clustering data, the minimum angular scale taken into account, and modelling of baryonic feedback effects. We conclude that the Euclid mission will be able to measure quantities related to the dark sector of particle physics with unprecedented sensitivity. This will provide important information for model building in high-energy physics. Any hint of a deviation from the minimal cold dark matter paradigm would have profound implications for cosmology and particle physics.

We forecast the expected population of active galactic nuclei (AGN) observable in the Euclid Wide Survey (EWS) and Euclid Deep Survey (EDS). Starting from an X-ray luminosity function (XLF), we generated volume-limited samples of the AGN expected in the Euclid survey footprints. Each AGN was assigned a spectral energy distribution (SED) appropriate for its X-ray luminosity and redshift, with perturbations sampled from empirical distributions. The photometric detectability of each AGN was assessed via mock observations of the assigned SED. We estimate 40 million AGN will be detectable in at least one Euclid band in the EWS and 0.24 million in the EDS, corresponding to surface densities of 2.8 × 103 deg-2 and 4.7 × 103 deg-2. The relative uncertainty on our expectation for Euclid detectable AGN is 6.7% for the EWS and 12.5% for the EDS, driven by the uncertainty of the XLF. Employing Euclid-only colour selection criteria on our simulated data we select a sample of 4.8 × 106 (331 deg-2 ) AGN in the EWS and 1.7 × 104 (346 deg-2 ) in the EDS, amounting to 10% and 8% of the AGN detectable in the EWS and EDS. Including ancillary Rubin/LSST bands improves the completeness and purity of AGN selection. These data roughly double the total number of selected AGN to comprise 21% and 15% of the Euclid detectable AGN in the EWS and EDS. The total expected sample of colour-selected AGN contains 6.0 × 106 (74%) unobscured AGN and 2.1 × 106 (26%) obscured AGN, covering 0.02 ≤ z ≲ 5.2 and 43 ≤ log10(Lbol/erg s-1 ) ≤ 47. With these simple colour cuts expected surface densities are already comparable to the yield of modern X-ray and mid-infrared surveys of similar area. The EWS sample is most comparable to the WISE C75 AGN selection and the EDS sample is most similar to the yield of the collated Spitzer cryogenic surveys when considering Euclid bands alone, or the XXL-3XLSS survey AGN sample when also considering selection with ancillary optical bands. We project that 15% (7.6%) of the total Euclid detectable population in the EWS (EDS) will exhibit X-ray fluxes that could be detected in the XMM-COSMOS survey, showing that the vast majority of Euclid-detected AGN would not be detectable in modern medium-depth X-ray surveys.