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R. Cledassou

Publications and source records attributed to R. Cledassou.

At least 19 recordsLinked to original sources

Euclid preparation. XLII. A unified catalogue-level reanalysis of weak lensing by galaxy clusters in five imaging surveys

Precise and accurate mass calibration is required to exploit galaxy clusters as astrophysical and cosmological probes in the Euclid era. Systematic errors in lensing signals by galaxy clusters can be empirically estimated by comparing different surveys with independent and uncorrelated systematics. To assess the robustness of the lensing results to systematic errors, we carried out end-to-end tests across different data sets. We performed a unified analysis at the catalogue level by leveraging the Euclid combined cluster and weak-lensing pipeline (COMB-CL). COMB-CL will measure weak lensing cluster masses for the Euclid Survey. Heterogeneous data sets from five independent, recent, lensing surveys (CHFTLenS, DES~SV1, HSC-SSP~S16a, KiDS~DR4, and RCSLenS), which exploited different shear and photometric redshift estimation algorithms, were analysed with a consistent pipeline under the same model assumptions. We performed a comparison of the amplitude of the reduced excess surface density and of the mass estimates using lenses from the Planck PSZ2 and SDSS redMaPPer cluster samples. Mass estimates agree with literature results collected in the LC2 catalogues. Mass accuracy was further investigated considering the AMICO detected clusters in the HSC-SSP XXL North field. The consistency of the data sets was tested using our unified analysis framework. We found agreement between independent surveys, at the level of systematic noise in Stage-III surveys or precursors. This indicates successful control over systematics. If such control continues in Stage-IV, Euclid will be able to measure the weak lensing masses of around 13000 (considering shot noise only) or 3000 (noise from shape and large-scale-structure) massive clusters with a signal-to-noise ratio greater than 3.

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Euclid: Identifying the reddest high-redshift galaxies in the Euclid Deep Fields with gradient-boosted trees

Dusty, distant, massive ($M_*\gtrsim 10^{11}\,\rm M_\odot$) galaxies are usually found to show a remarkable star-formation activity, contributing on the order of $25\%$ of the cosmic star-formation rate density at $z\approx3$--$5$, and up to $30\%$ at $z\sim7$ from ALMA observations. Nonetheless, they are elusive in classical optical surveys, and current near-infrared surveys are able to detect them only in very small sky areas. Since these objects have low space densities, deep and wide surveys are necessary to obtain statistically relevant results about them. Euclid will be potentially capable of delivering the required information, but, given the lack of spectroscopic features at these distances within its bands, it is still unclear if it will be possible to identify and characterize these objects. The goal of this work is to assess the capability of Euclid, together with ancillary optical and near-infrared data, to identify these distant, dusty and massive galaxies, based on broadband photometry. We used a gradient-boosting algorithm to predict both the redshift and spectral type of objects at high $z$. To perform such an analysis we make use of simulated photometric observations derived using the SPRITZ software. The gradient-boosting algorithm was found to be accurate in predicting both the redshift and spectral type of objects within the Euclid Deep Survey simulated catalog at $z>2$. In particular, we study the analog of HIEROs (i.e. sources with $H-[4.5]>2.25$), combining Euclid and Spitzer data at the depth of the Deep Fields. We found that the dusty population at $3\lesssim z\lesssim 7$ is well identified, with a redshift RMS and OLF of only $0.55$ and $8.5\%$ ($H_E\leq26$), respectively. Our findings suggest that with Euclid we will obtain meaningful insights into the role of massive and dusty galaxies in the cosmic star-formation rate over time.

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Euclid preparation: XLVIII. The pre-launch Science Ground Segment simulation framework

The European Space Agency's Euclid mission is one of the upcoming generation of large-scale cosmology surveys, which will map the large-scale structure in the Universe with unprecedented precision. The development and validation of the SGS pipeline requires state-of-the-art simulations with a high level of complexity and accuracy that include subtle instrumental features not accounted for previously as well as faster algorithms for the large-scale production of the expected Euclid data products. In this paper, we present the Euclid SGS simulation framework as applied in a large-scale end-to-end simulation exercise named Science Challenge 8. Our simulation pipeline enables the swift production of detailed image simulations for the construction and validation of the Euclid mission during its qualification phase and will serve as a reference throughout operations. Our end-to-end simulation framework starts with the production of a large cosmological N-body & mock galaxy catalogue simulation. We perform a selection of galaxies down to I_E=26 and 28 mag, respectively, for a Euclid Wide Survey spanning 165 deg^2 and a 1 deg^2 Euclid Deep Survey. We build realistic stellar density catalogues containing Milky Way-like stars down to H<26. Using the latest instrumental models for both the Euclid instruments and spacecraft as well as Euclid-like observing sequences, we emulate with high fidelity Euclid satellite imaging throughout the mission's lifetime. We present the SC8 data set consisting of overlapping visible and near-infrared Euclid Wide Survey and Euclid Deep Survey imaging and low-resolution spectroscopy along with ground-based. This extensive data set enables end-to-end testing of the entire ground segment data reduction and science analysis pipeline as well as the Euclid mission infrastructure, paving the way to future scientific and technical developments and enhancements.

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Euclid preparation. LII. Forecast impact of super-sample covariance on 3x2pt analysis with Euclid

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.

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Euclid preparation. XXXI. The effect of the variations in photometric passbands on photometric-redshift accuracy

The technique of photometric redshifts has become essential for the exploitation of multi-band extragalactic surveys. While the requirements on photo-zs for the study of galaxy evolution mostly pertain to the precision and to the fraction of outliers, the most stringent requirement in their use in cosmology is on the accuracy, with a level of bias at the sub-percent level for the Euclid cosmology mission. A separate, and challenging, calibration process is needed to control the bias at this level of accuracy. The bias in photo-zs has several distinct origins that may not always be easily overcome. We identify here one source of bias linked to the spatial or time variability of the passbands used to determine the photometric colours of galaxies. We first quantified the effect as observed on several well-known photometric cameras, and found in particular that, due to the properties of optical filters, the redshifts of off-axis sources are usually overestimated. We show using simple simulations that the detailed and complex changes in the shape can be mostly ignored and that it is sufficient to know the mean wavelength of the passbands of each photometric observation to correct almost exactly for this bias; the key point is that this mean wavelength is independent of the spectral energy distribution of the source}. We use this property to propose a correction that can be computationally efficiently implemented in some photo-z algorithms, in particular template-fitting. We verified that our algorithm, implemented in the new photo-z code Phosphoros, can effectively reduce the bias in photo-zs on real data using the CFHTLS T007 survey, with an average measured bias Delta z over the redshift range 0.4<z<0.7 decreasing by about 0.02, specifically from Delta z~0.04 to Delta z~0.02 around z=0.5. Our algorithm is also able to produce corrected photometry for other applications.

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Euclid: Cosmology forecasts from the void-galaxy cross-correlation function with reconstruction

We investigate the cosmological constraints that can be expected from measurement of the cross-correlation of galaxies with cosmic voids identified in the Euclid spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over $15\,000$ deg$^2$ of the sky in the redshift range $0.9\leq z<1.8$. We do this using simulated measurements obtained from the Flagship mock catalogue, the official Euclid mock that closely matches the expected properties of the spectroscopic data set. To mitigate anisotropic selection-bias effects, we use a velocity field reconstruction method to remove large-scale redshift-space distortions from the galaxy field before void-finding. This allows us to accurately model contributions to the observed anisotropy of the cross-correlation function arising from galaxy velocities around voids as well as from the Alcock-Paczynski effect, and we study the dependence of constraints on the efficiency of reconstruction. We find that Euclid voids will be able to constrain the ratio of the transverse comoving distance $D_{\rm M}$ and Hubble distance $D_{\rm H}$ to a relative precision of about $0.3\%$, and the growth rate $fσ_8$ to a precision of between $5\%$ and $8\%$ in each of four redshift bins covering the full redshift range. In the standard cosmological model, this translates to a statistical uncertainty $ΔΩ_\mathrm{m}=\pm0.0028$ on the matter density parameter from voids, better than can be achieved from either Euclid galaxy clustering and weak lensing individually. We also find that voids alone can measure the dark energy equation of state to $6\%$ precision.

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Euclid: Identification of asteroid streaks in simulated images using deep learning

Up to 150000 asteroids will be visible in the images of the ESA Euclid space telescope, and the instruments of Euclid offer multiband visual to near-infrared photometry and slitless spectra of these objects. Most asteroids will appear as streaks in the images. Due to the large number of images and asteroids, automated detection methods are needed. A non-machine-learning approach based on the StreakDet software was previously tested, but the results were not optimal for short and/or faint streaks. We set out to improve the capability to detect asteroid streaks in Euclid images by using deep learning. We built, trained, and tested a three-step machine-learning pipeline with simulated Euclid images. First, a convolutional neural network (CNN) detected streaks and their coordinates in full images, aiming to maximize the completeness (recall) of detections. Then, a recurrent neural network (RNN) merged snippets of long streaks detected in several parts by the CNN. Lastly, gradient-boosted trees (XGBoost) linked detected streaks between different Euclid exposures to reduce the number of false positives and improve the purity (precision) of the sample. The deep-learning pipeline surpasses the completeness and reaches a similar level of purity of a non-machine-learning pipeline based on the StreakDet software. Additionally, the deep-learning pipeline can detect asteroids 0.25-0.5 magnitudes fainter than StreakDet. The deep-learning pipeline could result in a 50% increase in the number of detected asteroids compared to the StreakDet software. There is still scope for further refinement, particularly in improving the accuracy of streak coordinates and enhancing the completeness of the final stage of the pipeline, which involves linking detections across multiple exposures.

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Euclid preparation. XXXIV. The effect of linear redshift-space distortions in photometric galaxy clustering and its cross-correlation with cosmic shear

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 $1\,\sigma$.

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Euclid: Modelling massive neutrinos in cosmology -- a code comparison

The measurement of the absolute neutrino mass scale from cosmological large-scale clustering data is one of the key science goals of the Euclid mission. Such a measurement relies on precise modelling of the impact of neutrinos on structure formation, which can be studied with $N$-body simulations. Here we present the results from a major code comparison effort to establish the maturity and reliability of numerical methods for treating massive neutrinos. The comparison includes eleven full $N$-body implementations (not all of them independent), two $N$-body schemes with approximate time integration, and four additional codes that directly predict or emulate the matter power spectrum. Using a common set of initial data we quantify the relative agreement on the nonlinear power spectrum of cold dark matter and baryons and, for the $N$-body codes, also the relative agreement on the bispectrum, halo mass function, and halo bias. We find that the different numerical implementations produce fully consistent results. We can therefore be confident that we can model the impact of massive neutrinos at the sub-percent level in the most common summary statistics. We also provide a code validation pipeline for future reference.

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Euclid Preparation XXXIII. Characterization of convolutional neural networks for the identification of galaxy-galaxy strong lensing events

Forthcoming imaging surveys will potentially increase the number of known galaxy-scale strong lenses by several orders of magnitude. For this to happen, images of tens of millions of galaxies will have to be inspected to identify potential candidates. In this context, deep learning techniques are particularly suitable for the finding patterns in large data sets, and convolutional neural networks (CNNs) in particular can efficiently process large volumes of images. We assess and compare the performance of three network architectures in the classification of strong lensing systems on the basis of their morphological characteristics. We train and test our models on different subsamples of a data set of forty thousand mock images, having characteristics similar to those expected in the wide survey planned with the ESA mission \Euclid, gradually including larger fractions of faint lenses. We also evaluate the importance of adding information about the colour difference between the lens and source galaxies by repeating the same training on single-band and multi-band images. Our models find samples of clear lenses with $\gtrsim 90\%$ precision and completeness, without significant differences in the performance of the three architectures. Nevertheless, when including lenses with fainter arcs in the training set, the three models' performance deteriorates with accuracy values of $\sim 0.87$ to $\sim 0.75$ depending on the model. Our analysis confirms the potential of the application of CNNs to the identification of galaxy-scale strong lenses. We suggest that specific training with separate classes of lenses might be needed for detecting the faint lenses since the addition of the colour information does not yield a significant improvement in the current analysis, with the accuracy ranging from $\sim 0.89$ to $\sim 0.78$ for the different models.

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Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics

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 of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($Ω_{\rm m}$, $σ_8$) 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 with $Euclid$. The data used in this analysis are publicly released with the paper.

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Euclid: Constraining linearly scale-independent modifications of gravity with the spectroscopic and photometric primary probes

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)

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Euclid: Constraints on f(R) cosmologies from the spectroscopic and photometric primary probes

$\textit{Euclid}$ will provide a powerful compilation of data including spectroscopic redshifts, the angular clustering of galaxies, weak lensing cosmic shear, and the cross-correlation of these last two photometric observables. In this study we extend recently presented $\textit{Euclid}$ forecasts into the Hu-Sawicki $f(R)$ cosmological model, a popular extension of the Hilbert-Einstein action that introduces an universal modified gravity force in a scale-dependent way. Our aim is to estimate how well future $\textit{Euclid}$ data will be able to constrain the extra parameter of the theory, $f_{R0}$, for the range in which this parameter is still allowed by current observations. For the spectroscopic probe, we use a phenomenological approach for the scale dependence of the growth of perturbations in the terms related to baryon acoustic oscillations and redshift-space distortions. For the photometric observables, we use a fitting formula that captures the modifications in the non-linear matter power spectrum caused by the $f(R)$ model. We show that, in an optimistic setting, and for a fiducial value of $f_{R0} = 5 \times 10^{-6}$, $\textit{Euclid}$ alone will be able to constrain the additional parameter $\log f_{R0}$ at the $3\%$ level, using spectroscopic galaxy clustering alone; at the $1.4\%$ level, using the combination of photometric probes on their own; and at the $1\%$ level, using the combination of spectroscopic and photometric observations. This last constraint corresponds to an error of the order of $6 \times 10^{-7}$ at the $1\sigma$ level on the model parameter $f_{R0} = 5 \times 10^{-6}$. We report also forecasted constraints for $f_{R0} = 5 \times 10^{-5}$ and $f_{R0} = 5 \times 10^{-7}$ and show that in the optimistic scenario, $\textit{Euclid}$ will be able to distinguish these models from $\Lambda\mathrm{CDM}$ at more than 3$\sigma$. (abridged)

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Euclid preparation. XXIX. Water ice in spacecraft part I: The physics of ice formation and contamination

Molecular contamination is a well-known problem in space flight. Water is the most common contaminant and alters numerous properties of a cryogenic optical system. Too much ice means that Euclid's calibration requirements and science goals cannot be met. Euclid must then be thermally decontaminated, a long and risky process. We need to understand how iced optics affect the data and when a decontamination is required. This is essential to build adequate calibration and survey plans, yet a comprehensive analysis in the context of an astrophysical space survey has not been done before. In this paper we look at other spacecraft with well-documented outgassing records, and we review the formation of thin ice films. A mix of amorphous and crystalline ices is expected for Euclid. Their surface topography depends on the competing energetic needs of the substrate-water and the water-water interfaces, and is hard to predict with current theories. We illustrate that with scanning-tunnelling and atomic-force microscope images. Industrial tools exist to estimate contamination, and we must understand their uncertainties. We find considerable knowledge errors on the diffusion and sublimation coefficients, limiting the accuracy of these tools. We developed a water transport model to compute contamination rates in Euclid, and find general agreement with industry estimates. Tests of the Euclid flight hardware in space simulators did not pick up contamination signals; our in-flight calibrations observations will be much more sensitive. We must understand the link between the amount of ice on the optics and its effect on Euclid's data. Little research is available about this link, possibly because other spacecraft can decontaminate easily, quenching the need for a deeper understanding. In our second paper we quantify the various effects of iced optics on spectrophotometric data.

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Euclid preparation. XXVII. A UV-NIR spectral atlas of compact planetary nebulae for wavelength calibration

The Euclid mission will conduct an extragalactic survey over 15000 deg$^2$ of the extragalactic sky. The spectroscopic channel of the Near-Infrared Spectrometer and Photometer (NISP) has a resolution of $R\sim450$ for its blue and red grisms that collectively cover the $0.93$--$1.89 $\micron;range. NISP will obtain spectroscopic redshifts for $3\times10^7$ galaxies for the experiments on galaxy clustering, baryonic acoustic oscillations, and redshift space distortion. The wavelength calibration must be accurate within $5$Åto avoid systematics in the redshifts and downstream cosmological parameters. The NISP pre-flight dispersion laws for the grisms were obtained on the ground using a Fabry-Perot etalon. Launch vibrations, zero gravity conditions, and thermal stabilisation may alter these dispersion laws, requiring an in-flight recalibration. To this end, we use the emission lines in the spectra of compact planetary nebulae (PNe), which were selected from a PN data base. To ensure completeness of the PN sample, we developed a novel technique to identify compact and strong line emitters in Gaia spectroscopic data using the Gaia spectra shape coefficients. We obtained VLT/X-SHOOTER spectra from $0.3$ to $2.5$ \micron;for 19 PNe in excellent seeing conditions and a wide slit, mimicking Euclid's slitless spectroscopy mode but with 10 times higher spectral resolution. Additional observations of one northern PN were obtained in the $0.80$--$1.90$ \micron range with the GMOS and GNIRS instruments at the Gemini North observatory. The collected spectra were combined into an atlas of heliocentric vacuum wavelengths with a joint statistical and systematic accuracy of 0.1 Åin the optical and 0.3 Åin the near-infrared. The wavelength atlas and the related 1D and 2D spectra are made publicly available.

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Euclid: Validation of the MontePython forecasting tools

The Euclid mission of the European Space Agency will perform a survey of weak lensing cosmic shear and galaxy clustering in order to constrain cosmological models and fundamental physics. We expand and adjust the mock Euclid likelihoods of the MontePython software in order to match the exact recipes used in previous Euclid Fisher matrix forecasts for several probes: weak lensing cosmic shear, photometric galaxy clustering, the cross-correlation between the latter observables, and spectroscopic galaxy clustering. We also establish which precision settings are required when running the Einstein-Boltzmann solvers CLASS and CAMB in the context of Euclid. For the minimal cosmological model, extended to include dynamical dark energy, we perform Fisher matrix forecasts based directly on a numerical evaluation of second derivatives of the likelihood with respect to model parameters. We compare our results with those of other forecasting methods and tools. We show that such MontePython forecasts agree very well with previous Fisher forecasts published by the Euclid Collaboration, and also, with new forecasts produced by the CosmicFish code, now interfaced directly with the two Einstein-Boltzmann solvers CAMB and CLASS. Moreover, to establish the validity of the Gaussian approximation, we show that the Fisher matrix marginal error contours coincide with the credible regions obtained when running Monte Carlo Markov Chains with MontePython while using the exact same mock likelihoods. The new Euclid forecast pipelines presented here are ready for use with additional cosmological parameters, in order to explore extended cosmological models.

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Euclid preparation. XXIV. Calibration of the halo mass function in $Λ(ν)$CDM cosmologies

Euclid's photometric galaxy cluster survey has the potential to be a very competitive cosmological probe. The main cosmological probe with observations of clusters is their number count, within which the halo mass function (HMF) is a key theoretical quantity. We present a new calibration of the analytic HMF, at the level of accuracy and precision required for the uncertainty in this quantity to be subdominant with respect to other sources of uncertainty in recovering cosmological parameters from Euclid cluster counts. Our model is calibrated against a suite of N-body simulations using a Bayesian approach taking into account systematic errors arising from numerical effects in the simulation. First, we test the convergence of HMF predictions from different N-body codes, by using initial conditions generated with different orders of Lagrangian Perturbation theory, and adopting different simulation box sizes and mass resolution. Then, we quantify the effect of using different halo-finder algorithms, and how the resulting differences propagate to the cosmological constraints. In order to trace the violation of universality in the HMF, we also analyse simulations based on initial conditions characterised by scale-free power spectra with different spectral indexes, assuming both Einstein--de Sitter and standard $Λ$CDM expansion histories. Based on these results, we construct a fitting function for the HMF that we demonstrate to be sub-percent accurate in reproducing results from 9 different variants of the $Λ$CDM model including massive neutrinos cosmologies. The calibration systematic uncertainty is largely sub-dominant with respect to the expected precision of future mass-observation relations; with the only notable exception of the effect due to the halo finder, that could lead to biased cosmological inference.

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Euclid: Calibrating photometric redshifts with spectroscopic cross-correlations

Cosmological constraints from key probes of the Euclid imaging survey rely critically on the accurate determination of the true redshift distributions, $n(z)$, of tomographic redshift bins. We determine whether the mean redshift, $ $, of ten Euclid tomographic redshift bins can be calibrated to the Euclid target uncertainties of $σ( )<0.002\,(1+z)$ via cross-correlation, with spectroscopic samples akin to those from the Baryon Oscillation Spectroscopic Survey (BOSS), Dark Energy Spectroscopic Instrument (DESI), and Euclid's NISP spectroscopic survey. We construct mock Euclid and spectroscopic galaxy samples from the Flagship simulation and measure small-scale clustering redshifts up to redshift $z<1.8$ with an algorithm that performs well on current galaxy survey data. The clustering measurements are then fitted to two $n(z)$ models: one is the true $n(z)$ with a free mean; the other a Gaussian Process modified to be restricted to non-negative values. We show that $ $ is measured in each tomographic redshift bin to an accuracy of order 0.01 or better. By measuring the clustering redshifts on subsets of the full Flagship area, we construct scaling relations that allow us to extrapolate the method performance to larger sky areas than are currently available in the mock. For the full expected Euclid, BOSS, and DESI overlap region of approximately 6000 deg$^{2}$, the uncertainties attainable by clustering redshifts exceeds the Euclid requirement by at least a factor of three for both $n(z)$ models considered, although systematic biases limit the accuracy. Clustering redshifts are an extremely effective method for redshift calibration for Euclid if the sources of systematic biases can be determined and removed, or calibrated-out with sufficiently realistic simulations. We outline possible future work, in particular an extension to higher redshifts with quasar reference samples.

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