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We characterize the ability of the Dark Energy Camera (DECam) to perform relative astrometry across its 500 Mpix, 3-deg2 science field of view and across four years of operation. This is done using internal comparisons of ∼4 × 107 measurements of high signal-to-noise ratio stellar images obtained in repeat visits to fields of moderate stellar density, with the telescope dithered to move the sources around the array. An empirical astrometric model includes terms for optical distortions; stray electric fields in the CCD detectors; chromatic terms in the instrumental and atmospheric optics; shifts in CCD relative positions of up to 10 m when the DECam temperature cycles; and low-order distortions to each exposure from changes in atmospheric refraction and telescope alignment. Errors in this astrometric model are dominated by stochastic variations with typical amplitudes of 10-30 mas (in a 30 s exposure) and 5′-10′ coherence length, plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of these atmospheric distortions is not closely related to the seeing. Given an astrometric reference catalog at density 0.7 arcmin − 2 , e.g., from Gaia, the typical atmospheric distortions can be interpolated to 7 mas rms accuracy (for 30 s exposures) with 1 ′ coherence length in residual errors. Remaining detectable error contributors are 2-4 mas rms from unmodelled stray electric fields in the devices, and another 2-4 mas rms from focal plane shifts between camera thermal cycles. Thus the astrometric solution for a single DECam exposure is accurate to 3-6 mas ( 0.02 pixels, or 300 nm) on the focal plane, plus the stochastic atmospheric distortion.

We characterize the ability of the Dark Energy Camera (DECam) to perform relative astrometry across its 500 Mpix, 3-deg² science field of view and across four years of operation. This is done using internal comparisons of ∼4 × 10⁷ measurements of high signal-to-noise ratio stellar images obtained in repeat visits to fields of moderate stellar density, with the telescope dithered to move the sources around the array. An empirical astrometric model includes terms for optical distortions; stray electric fields in the CCD detectors; chromatic terms in the instrumental and atmospheric optics; shifts in CCD relative positions of up to ≈10 μm when the DECam temperature cycles; and low-order distortions to each exposure from changes in atmospheric refraction and telescope alignment. Errors in this astrometric model are dominated by stochastic variations with typical amplitudes of 10–30 mas (in a 30 s exposure) and 5′–10′ coherence length, plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of these atmospheric distortions is not closely related to the seeing. Given an astrometric reference catalog at density ≈0.7 arcmin−2, e.g., from Gaia, the typical atmospheric distortions can be interpolated to ≈7 mas rms accuracy (for 30 s exposures) with 1′ coherence length in residual errors. Remaining detectable error contributors are 2–4 mas rms from unmodelled stray electric fields in the devices, and another 2–4 mas rms from focal plane shifts between camera thermal cycles. Thus the astrometric solution for a single DECam exposure is accurate to 3–6 mas (≈0.02 pixels, or ≈300 nm) on the focal plane, plus the stochastic atmospheric distortion.

We characterize the ability of the Dark Energy Camera (DECam) to perform relative astrometry across its 500 Mpix, 3-deg2 science field of view and across four years of operation. This is done using internal comparisons of ~4 × 107 measurements of high signal-to-noise ratio stellar images obtained in repeat visits to fields of moderate stellar density, with the telescope dithered to move the sources around the array. An empirical astrometric model includes terms for optical distortions; stray electric fields in the CCD detectors; chromatic terms in the instrumental and atmospheric optics; shifts in CCD relative positions of up to ≈10 μm when the DECam temperature cycles; and low-order distortions to each exposure from changes in atmospheric refraction and telescope alignment. Errors in this astrometric model are dominated by stochastic variations with typical amplitudes of 10–30 mas (in a 30 s exposure) and 5'–10' coherence length, plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of these atmospheric distortions is not closely related to the seeing. Given an astrometric reference catalog at density ≈ 0.7 arcmin-2, e.g., from Gaia, the typical atmospheric distortions can be interpolated to ≈7 mas rms accuracy (for 30 s exposures) with $1^{\\prime} $ coherence length in residual errors. Remaining detectable error contributors are 2–4 mas rms from unmodelled stray electric fields in the devices, and another 2–4 mas rms from focal plane shifts between camera thermal cycles. Thus the astrometric solution for a single DECam exposure is accurate to 3–6 mas (≈0.02 pixels, or ≈300 nm) on the focal plane, plus the stochastic atmospheric distortion.

We use a recently introduced statistic called {\\em Integrated Bispectrum} (IB) to probe the gravity-induced non-Gaussianity at the level of the bispectrum from weak lensing convergence or \\(\\kappa\\) maps. We generalize the concept of the IB to spherical coordinates. This result is next connected to the response function approach. Finally, we use the Euclid Flagship simulations to compute the IB as a function of redshift and wave number. We also outline how the IB can be computed using a variety of analytical approaches including the ones based on Effective Field Theory (EFT), {\\em Halo models} and models based on the {\\em Separate Universe approach} in projection or two-dimension (2D). Comparing these results against simulations we find that the existing theoretical models tend to over-predict the numerical value of the IB. We emphasize the role of the finite volume effect in the numerical estimation of the IB. We introduced the concept of squeezed and collapsed tripsectrum for 2D \\(\\kappa\\) maps. We derive the IB for many parameterized theories of modified gravity including the Horndeskii and beyond-Horndeskii theories specifically for the non-degenerate scenarios that are also known as the Gleyzes-Langlois-Piazza-Venizzi or GPLV theories. In addition, the cosmological models with clustering quintessence and models involving massive neutrinos are also derived.

Deviations from Gaussianity in the distribution of the fields probed by large-scale structure surveys generate additional terms in the data covariance matrix, increasing the uncertainties in the measurement of the cosmological parameters. Super-sample covariance (SSC) is among the largest of these non-Gaussian contributions, with the potential to significantly degrade constraints on some of the parameters of the cosmological model under study - especially for weak lensing cosmic shear. We compute and validate the impact of SSC on the forecast uncertainties on the cosmological parameters for the Euclid photometric survey, obtained with a Fisher matrix analysis, both considering the Gaussian covariance alone and adding the SSC term - computed through the public code \\(\\tt{PySSC}\\). The photometric probes are considered in isolation and combined in the '3\\(\\times\\)2pt' analysis. We find the SSC impact to be non-negligible - halving the Figure of Merit of the dark energy parameters \\((w_0, w_a)\\) in the 3\\(\\times\\)2pt case and substantially increasing the uncertainties on \\(\\Omega_{{\\rm m}, 0}, w_0\\), and \\(\\sigma_8\\) for cosmic shear; photometric galaxy clustering, on the other hand, is less affected due to the lower probe response. The relative impact of SSC does not show significant changes under variations of the redshift binning scheme, while it is smaller for weak lensing when marginalising over the multiplicative shear bias nuisance parameters, which also leads to poorer constraints on the cosmological parameters. Finally, we explore how the use of prior information on the shear and galaxy bias changes the SSC impact. Improving shear bias priors does not have a significant impact, while galaxy bias must be calibrated to sub-percent level to increase the Figure of Merit by the large amount needed to achieve the value when SSC is not included.

LensMC is a weak lensing shear measurement method developed for Euclid and Stage-IV surveys. It is based on forward modelling in order to deal with convolution by a point spread function (PSF) with comparable size to many galaxies; sampling the posterior distribution of galaxy parameters via Markov Chain Monte Carlo; and marginalisation over nuisance parameters for each of the 1.5 billion galaxies observed by Euclid. We quantified the scientific performance through high-fidelity images based on the Euclid Flagship simulations and emulation of the Euclid VIS images; realistic clustering with a mean surface number density of 250 arcmin\\(^{-2}\\) (\\(I_{\\rm E}<29.5\\)) for galaxies, and 6 arcmin\\(^{-2}\\) (\\(I_{\\rm E}<26\\)) for stars; and a diffraction-limited chromatic PSF with a full width at half maximum of \\(0.^{\\!\\prime\\prime}2\\) and spatial variation across the field of view. LensMC measured objects with a density of 90 arcmin\\(^{-2}\\) (\\(I_{\\rm E}<26.5\\)) in 4500 deg\\(^2\\). The total shear bias was broken down into measurement (our main focus here) and selection effects (which will be addressed elsewhere). We found measurement multiplicative and additive biases of \\(m_1=(-3.6\\pm0.2)\\times10^{-3}\\), \\(m_2=(-4.3\\pm0.2)\\times10^{-3}\\), \\(c_1=(-1.78\\pm0.03)\\times10^{-4}\\), \\(c_2=(0.09\\pm0.03)\\times10^{-4}\\); a large detection bias with a multiplicative component of \\(1.2\\times10^{-2}\\) and an additive component of \\(-3\\times10^{-4}\\); and a measurement PSF leakage of \\(\\alpha_1=(-9\\pm3)\\times10^{-4}\\) and \\(\\alpha_2=(2\\pm3)\\times10^{-4}\\). When model bias is suppressed, the obtained measurement biases are close to Euclid requirement and largely dominated by undetected faint galaxies (\\(-5\\times10^{-3}\\)). Although significant, model bias will be straightforward to calibrate given the weak sensitivity. LensMC is publicly available at https://gitlab.com/gcongedo/LensMC

Euclid will collect an enormous amount of data during the mission's lifetime, observing billions of galaxies in the extragalactic sky. Along with traditional template-fitting methods, numerous machine learning algorithms have been presented for computing their photometric redshifts and physical parameters (PPs), requiring significantly less computing effort while producing equivalent performance measures. However, their performance is limited by the quality and amount of input information, to the point where the recovery of some well-established physical relationships between parameters might not be guaranteed. To forecast the reliability of Euclid photo-\\(z\\)s and PPs calculations, we produced two mock catalogs simulating Euclid photometry. We simulated the Euclid Wide Survey (EWS) and Euclid Deep Fields (EDF). We tested the performance of a template-fitting algorithm (Phosphoros) and four ML methods in recovering photo-\\(z\\)s, PPs (stellar masses and star formation rates), and the SFMS. To mimic the Euclid processing as closely as possible, the models were trained with Phosphoros-recovered labels. For the EWS, we found that the best results are achieved with a mixed labels approach, training the models with wide survey features and labels from the Phosphoros results on deeper photometry, that is, with the best possible set of labels for a given photometry. This imposes a prior, helping the models to better discern cases in degenerate regions of feature space, that is, when galaxies have similar magnitudes and colors but different redshifts and PPs, with performance metrics even better than those found with Phosphoros. We found no more than 3% performance degradation using a COSMOS-like reference sample or removing u band data, which will not be available until after data release DR1. The best results are obtained for the EDF, with appropriate recovery of photo-\\(z\\), PPs, and the SFMS.

The future Euclid space satellite mission will offer an invaluable opportunity to constrain modifications to Einstein's general relativity at cosmic scales. We focus on modified gravity models characterised, at linear scales, by a scale-independent growth of perturbations while featuring different testable types of derivative screening mechanisms at smaller non-linear scales. We considered three specific models, namely JBD, a scalar-tensor theory with a flat potential, the nDGP gravity, a braneworld model in which our Universe is a four-dimensional brane embedded in a five-dimensional Minkowski space-time, and \\(k\\)-mouflage (KM) gravity, an extension of \\(k\\)-essence scenarios with a universal coupling of the scalar field to matter. In preparation for real data, we provide forecasts from spectroscopic and photometric primary probes by Euclid on the cosmological parameters and the additional parameters of the models, respectively, \\(\\omega_{\\rm BD}\\), \\(\\Omega_{\\rm rc}\\) and \\(\\epsilon_{2,0}\\). The forecast analysis employs the Fisher matrix method applied to weak lensing (WL); photometric galaxy clustering (GCph), spectroscopic galaxy clustering (GCsp) and the cross-correlation (XC) between GCph and WL. In an optimistic setting at 68.3\\% confidence interval, we find the following percentage relative errors with Euclid alone: for \\(\\log_{10}{\\omega_{\\rm BD}}\\), with a fiducial value of \\(\\omega_{\\rm BD}=800\\), 27.1\\% using GCsp alone, 3.6\\% using GCph+WL+XC and 3.2\\% using GCph+WL+XC+GCsp; for \\(\\log_{10}{\\Omega_{\\rm rc}}\\), with a fiducial value of \\(\\Omega_{\\rm rc}=0.25\\), we find 93.4\\%, 20\\% and 15\\% respectively; and finally, for \\(\\epsilon_{2,0}=-0.04\\), we find 3.4\\%, 0.15\\%, and 0.14\\%. (abridged)

The cosmological surveys that are planned for the current decade will provide us with unparalleled observations of the distribution of galaxies on cosmic scales, by means of which we can probe the underlying large-scale structure (LSS) of the Universe. This will allow us to test the concordance cosmological model and its extensions. However, precision pushes us to high levels of accuracy in the theoretical modelling of the LSS observables, so that no biases are introduced into the estimation of the cosmological parameters. In particular, effects such as redshift-space distortions (RSD) can become relevant in the computation of harmonic-space power spectra even for the clustering of the photometrically selected galaxies, as has previously been shown in literature. In this work, we investigate the contribution of linear RSD, as formulated in the Limber approximation by a previous work, in forecast cosmological analyses with the photometric galaxy sample of the Euclid survey. We aim to assess their impact and to quantify the bias on the measurement of cosmological parameters that would be caused if this effect were neglected. We performed this task by producing mock power spectra for photometric galaxy clustering and weak lensing, as is expected to be obtained from the Euclid survey. We then used a Markov chain Monte Carlo approach to obtain the posterior distributions of cosmological parameters from these simulated observations. When the linear RSD is neglected, significant biases are caused when galaxy correlations are used alone and when they are combined with cosmic shear in the so-called 3\\(\\times\\)2pt approach. These biases can be equivalent to as much as \\(5\\,\\sigma\\) when an underlying \\(\\Lambda\\)CDM cosmology is assumed. When the cosmological model is extended to include the equation-of-state parameters of dark energy, the extension parameters can be shifted by more than \\(1\\,\\sigma\\).

We present an alternative calibration of the MagLim lens sample redshift distributions from the Dark Energy Survey (DES) first three years of data (Y3). The new calibration is based on a combination of a Self-Organising Maps based scheme and clustering redshifts to estimate redshift distributions and inherent uncertainties, which is expected to be more accurate than the original DES Y3 redshift calibration of the lens sample. We describe in detail the methodology, we validate it on simulations and discuss the main effects dominating our error budget. The new calibration is in fair agreement with the fiducial DES Y3 redshift distributions calibration, with only mild differences (\\(<3\\sigma\\)) in the means and widths of the distributions. We study the impact of this new calibration on cosmological constraints, analysing DES Y3 galaxy clustering and galaxy-galaxy lensing measurements, assuming a \\(\\Lambda\\)CDM cosmology. We obtain \\(\\Omega_{\\rm m} = 0.30\\pm 0.04\\), \\(\\sigma_8 = 0.81\\pm 0.07 \\) and \\(S_8 = 0.81\\pm 0.04\\), which implies a \\(\\sim 0.4\\sigma\\) shift in the \\(\\Omega_{\\rm}-S_8\\) plane compared to the fiducial DES Y3 results, highlighting the importance of the redshift calibration of the lens sample in multi-probe cosmological analyses.