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.

Gravitational waves can provide an accurate measurement of the luminosity distance to the source but cannot provide the source redshift unless the degeneracy between mass and redshift can be broken. This makes it essential to infer the redshift of the source independently to measure the expansion history of the Universe. We show that by exploiting the clustering scale of the gravitational wave sources with galaxies of a known redshift, we can infer the expansion history from redshift unknown gravitational wave sources. By using gravitational wave sources of unknown redshift that are detectable from the network of gravitational wave detectors with Advanced LIGO design sensitivity, we will be able to obtain accurate and precise measurements of the local Hubble constant, the expansion history of the Universe, and the gravitational wave bias parameter, which captures the distribution of gravitational wave sources with respect to the redshift tracer distribution. While we showcase its application to low redshift gravitational waves, this technique will be applicable also to the high redshift gravitational wave sources detectable from Laser Interferometer Space Antenna (LISA), Cosmic Explorer (CE), and Einstein Telescope (ET). Moreover, this method will also be applicable to samples of supernovae and fast radio bursts with unknown or photometric redshifts.

The cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) are two of the most robust observations in cosmology. The recent BAO measurements from the DESI collaboration have presented, for the first time, inconsistency between BAO and CMB within the standard cosmological model ΛCDM, indicating a preference for dynamical dark energy over a cosmological constant. We analyze the theoretical implication of the DESI BAO observation for dark energy and gravity employing a nonparametric reconstruction approach for both the dark energy equation of state w_{DE}(a) and the effective field theory coefficients. We find that the DESI data can rule out quintessence dark energy by indicating a crossing of the phantom divide at z≲1. Furthermore, when analyzed within the broad context of Horndeski gravity which includes general relativity and many known modified gravity theories such as generalized Galileons, f(R), and Brans-Dicke, our result implies that gravity should be nonminimally coupled to explain the observations, establishing the DESI result as the first hint of modified gravity. Based on these insights, we propose the thawing gravity model to explain the nonminimal coupling and phantom crossing indicated by observation, which also fits better to DESI BAO, CMB, and type Ia Supernovae data than ΛCDM.

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.