Aims. The Euclid space telescope will measure the shapes and redshifts of galaxies to reconstruct the expansion history of the Universe and the growth of cosmic structures. The estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on various individual methodologies and numerical implementations, which were developed for different observational probes and for the combination thereof. In this paper we present validated forecasts, which combine both theoretical and observational ingredients for different cosmological probes. This work is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts. Methods. We describe in detail the methods adopted for Fisher matrix forecasts, which were applied to galaxy clustering, weak lensing, and the combination thereof. We estimated the required accuracy for Euclid forecasts and outline a methodology for their development. We then compare and improve different numerical implementations, reaching uncertainties on the errors of cosmological parameters that are less than the required precision in all cases. Furthermore, we provide details on the validated implementations, some of which are made publicly available, in different programming languages, together with a reference training-set of input and output matrices for a set of specific models. These can be used by the reader to validate their own implementations if required. Results. We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setting, for example flat or non-flat spatial cosmologies, or different cuts at non-linear scales. The numerical implementations are now reliable for these settings. We present the results for an optimistic and a pessimistic choice for these types of settings. We demonstrate that the impact of cross-correlations is particularly relevant for models beyond a cosmological constant and may allow us to increase the dark energy figure of merit by at least a factor of three.

Euclid is a mission of the European Space Agency that is designed to constrain the properties of dark energy and gravity via weak gravitational lensing and galaxy clustering. It will carry out a wide area imaging and spectroscopy survey (the Euclid Wide Survey: EWS) in visible and near-infrared bands, covering approximately 15 000 deg2 of extragalactic sky in six years. The wide-field telescope and instruments are optimised for pristine point spread function and reduced stray light, producing very crisp images. This paper presents the building of the Euclid reference survey: the sequence of pointings of EWS, deep fields, and calibration fields, as well as spacecraft movements followed by Euclid as it operates in a step-and-stare mode from its orbit around the Lagrange point L2. Each EWS pointing has four dithered frames; we simulated the dither pattern at the pixel level to analyse the effective coverage. We used up-to-date models for the sky background to define the Euclid region-of-interest (RoI). The building of the reference survey is highly constrained from calibration cadences, spacecraft constraints, and background levels; synergies with ground-based coverage were also considered. Via purposely built software, we first generated a schedule for the calibrations and deep fields observations. On a second stage, the RoI was tiled and scheduled with EWS observations, using an algorithm optimised to prioritise the best sky areas, produce a compact coverage, and ensure thermal stability. The result is the optimised reference survey RSD_2021A, which fulfils all constraints and is a good proxy for the final solution. The current EWS covers ≈14 500 deg2. The limiting AB magnitudes (5σ point-like source) achieved in its footprint are estimated to be 26.2 (visible band IE) and 24.5 (for near infrared bands YE, JE, HE); for spectroscopy, the Hα line flux limit is 2 × 10−16 erg−1 cm−2 s−1 at 1600 nm; and for diffuse emission, the surface brightness limits are 29.8 (visible band) and 28.4 (near infrared bands) mag arcsec−2.

Context. While Euclid is an ESA mission specifically designed to investigate the nature of dark energy and dark matter, the planned unprecedented combination of survey area (∼15 000 deg2), spatial resolution, low sky-background, and depth also make Euclid an excellent space observatory for the study of the low surface brightness Universe. Scientific exploitation of the extended low surface brightness structures requires dedicated calibration procedures that are yet to be tested. Aims. We investigate the capabilities of Euclid to detect extended low surface brightness structure by identifying and quantifying sky-background sources and stray-light contamination. We test the feasibility of generating sky flat-fields to reduce large-scale residual gradients in order to reveal the extended emission of galaxies observed in the Euclid survey. Methods. We simulated a realistic set of Euclid/VIS observations, taking into account both instrumental and astronomical sources of contamination, including cosmic rays, stray-light, zodiacal light, interstellar medium, and the cosmic infrared background, while simulating the effects of background sources in the field of view. Results. We demonstrate that a combination of calibration lamps, sky flats, and self-calibration would enable recovery of emission at a limiting surface brightness magnitude of μlim = 29.5−0.27+0.08 mag arcsec−2 (3σ, 10 × 10 arcsec2) in the Wide Survey, and it would reach regions deeper by 2 mag in the Deep Surveys. Conclusions.Euclid/VIS has the potential to be an excellent low surface brightness observatory. Covering the gap between pixel-to-pixel calibration lamp flats and self-calibration observations for large scales, the application of sky flat-fielding will enhance the sensitivity of the VIS detector at scales larger than 1″, up to the size of the field of view, enabling Euclid to detect extended surface brightness structures below μlim = 31 mag arcsec−2 and beyond.

The Euclid space telescope will survey a large dataset of cosmic voids traced by dense samples of galaxies. In this work we estimate its expected performance when exploiting angular photometric void clustering, galaxy weak lensing, and their cross-correlation. To this aim, we implemented a Fisher matrix approach tailored for voids from the Euclid photometric dataset and we present the first forecasts on cosmological parameters that include the void-lensing correlation. We examined two different probe settings, pessimistic and optimistic, both for void clustering and galaxy lensing. We carried out forecast analyses in four model cosmologies, accounting for a varying total neutrino mass, M ν , and a dynamical dark energy (DE) equation of state, w(z), described by the popular Chevallier-Polarski-Linder parametrization. We find that void clustering constraints on h and Ω b are competitive with galaxy lensing alone, while errors on n s decrease thanks to the orthogonality of the two probes in the 2D-projected parameter space. We also note that, as a whole, with respect to assuming the two probes as independent, the inclusion of the void-lensing crosscorrelation signal improves parameter constraints by 10 − 15%, and enhances the joint void clustering and galaxy lensing figure of merit (FoM) by 10% and 25%, in the pessimistic and optimistic scenarios, respectively. Finally, when further combining with the spectroscopic galaxy clustering, assumed as an independent probe, we find that, in the most competitive case, the FoM increases by a factor of 4 with respect to the combination of weak lensing and spectroscopic galaxy clustering taken as independent probes. The forecasts presented in this work show that photometric void clustering and its cross-correlation with galaxy lensing deserve to be exploited in the data analysis of the Euclid galaxy survey and promise to improve its constraining power, especially on h, Ω b , the neutrino mass, and the DE evolution.