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V. F. Cardone

Publications and source records attributed to V. F. Cardone.

At least 37 records · Page 2Linked to original sources

Euclid preparation. XCVIII. Cosmology Likelihood for Observables in Euclid (CLOE). 5: Extensions beyond the standard modelling of theoretical probes and systematic effects

Euclid is expected to establish new state-of-the-art constraints on extensions beyond the standard LCDM cosmological model by measuring the positions and shapes of billions of galaxies. Specifically, its goal is to shed light on the nature of dark matter and dark energy. Achieving this requires developing and validating advanced statistical tools and theoretical prediction software capable of testing extensions of the LCDM model. In this work, we describe how the Euclid likelihood pipeline, Cosmology Likelihood for Observables in Euclid (CLOE), has been extended to accommodate alternative cosmological models and to refine the theoretical modelling of Euclid primary probes. In particular, we detail modifications made to CLOE to incorporate the magnification bias term into the spectroscopic two-point correlation function of galaxy clustering. Additionally, we explain the adaptations made to CLOE's implementation of Euclid primary photometric probes to account for massive neutrinos and modified gravity extensions. Finally, we present the validation of these CLOE modifications through dedicated forecasts on synthetic Euclid-like data by sampling the full posterior distribution and comparing with the results of previous literature. In conclusion, we have identified in this work several functionalities with regards to beyond-LCDM modelling that could be further improved within CLOE, and outline potential research directions to enhance pipeline efficiency and flexibility through novel inference and machine learning techniques.

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Euclid preparation. XCVI. Cosmology Likelihood for Observables in Euclid (CLOE). 3. Inference and Forecasts

The Euclid mission aims to measure the positions, shapes, and redshifts of over a billion galaxies to provide unprecedented constraints on the nature of dark matter and dark energy. Achieving this goal requires a continuous reassessment of the mission's scientific performance, particularly in terms of its ability to constrain cosmological parameters, as our understanding of how to model large-scale structure observables improves. In this study, we present the first scientific forecasts using CLOE (Cosmology Likelihood for Observables in Euclid), a dedicated Euclid cosmological pipeline developed to support this endeavour. Using advanced Bayesian inference techniques applied to synthetic Euclid-like data, we sample the posterior distribution of cosmological and nuisance parameters across a variety of cosmological models and Euclid primary probes: cosmic shear, angular photometric galaxy clustering, galaxy-galaxy lensing, and spectroscopic galaxy clustering. We validate the capability of CLOE to produce reliable cosmological forecasts, showcasing Euclid's potential to achieve a figure of merit for the dark energy parameters $w_0$ and $w_a$ exceeding 400 when combining all primary probes. Furthermore, we illustrate the behaviour of the posterior probability distribution of the parameters of interest given different priors and scale cuts. Finally, we emphasise the importance of addressing computational challenges, proposing further exploration of innovative data science techniques to efficiently navigate the Euclid high-dimensional parameter space in upcoming cosmological data releases.

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Euclid preparation. Three-dimensional galaxy clustering in configuration space: Three-point correlation function estimation

Higher-order correlation functions are firmly established as a fundamental tool for the statistical analysis of clustering in modern galaxy surveys. It was demonstrated that they greatly enrich the information content extracted by two-point statistics, allowing us to break the degeneracies between model parameters and constrain departures from Gaussianity. This paper presents the statistical estimators adopted to evaluate the galaxy three-point correlation function and its numerical implementation within the data analysis pipeline of the Euclid Science Ground Segment. Two different algorithms are adopted to count triplets: a direct and exact counting method capable of providing a robust three-point correlation function measurement for any triangular configuration, and a more efficient method based on spherical harmonic decomposition, designed to address the computational challenges of measuring the three-point statistics for data sets as large as those of the final Euclid survey. The spherical harmonic decomposition estimates the Legendre coefficients of the three-point correlation function up to a finite expansion order. Despite being an approximation, the three-point function measured with this approach satisfies the scientific requirements of the mission. We also introduce, implement, and validate the random split technique, which reduces the computational cost of counting triplets in the reference random sample by a factor of 10, without significantly compromising numerical accuracy. We evaluated the robustness, precision, and accuracy of the numerical estimates through an extensive campaign of validation tests, the results of which are presented. Finally, we quantify the computational requirements and their scaling with the expected size of Euclid data set, showing that a complete three-point analysis of the final Euclid survey is within computational reach.

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Euclid preparation. Refining input galaxy shape distributions for shear calibration simulations

The Euclid Wide Survey (EWS) will cover the majority of the extragalactic sky with a resolution similar to the Hubble Space Telescope. This unprecedented data set will introduce a new era of precision cosmology. However, systematic effects need to be controlled better than ever. One of the sources of systematic uncertainties in weak gravitational lensing are biases introduced during the shear measurement. Determining these biases precisely allows the calibration of cosmological measurements to within Euclid's required accuracy. The simulations that are used to determine such biases, need to resemble the real observations. In this work, we aim to learn distributions of galaxy shape parameters from real Euclid data and use the new information to augment the morphological information in the Flagship galaxy mock catalogue. The morphology is extracted using single and double-Sérsic model fits to the real data, for which we use SourceXtractor++. We train our pipeline on deep Euclid observations of a field with rich auxiliary data and then use it to simulate EWS-like data. In these simulations we compare the multiplicative bias between the morphology from the Flagship catalogue, the trained single-Sérsic morphology, and the trained double-Sérsic morphology. We find that the image simulations with the updated morphology result in a percent-level change in the multiplicative shear bias compared to the original morphology from Flagship. This bias exceeds Euclid's tight error budget by a factor of five and underlines the need for this work. Furthermore, we study the sensitivity of the multiplicative bias to key morphological parameters and show that our approach satisfies the requirements for the cosmology analysis with the first data release of Euclid.

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Euclid preparation. LXXXIX. Accurate and precise data-driven angular power spectrum covariances

We develop techniques for generating accurate and precise internal covariances for measurements of clustering and weak-lensing angular power spectra. These methods have been designed to produce non-singular and unbiased covariances for Euclid's large anticipated data vector and will be critical for validation against observational systematic effects. We constructed jackknife segments that are equal in area to a high precision by adapting the binary space partition algorithm to work on arbitrarily shaped regions on the unit sphere. Jackknife estimates of the covariances are internally derived and require no assumptions about cosmology or galaxy population and bias. Our covariance estimation, called DICES (Debiased Internal Covariance Estimation with Shrinkage), first estimated a noisy covariance through conventional delete-1 jackknife resampling. This was followed by linear shrinkage of the empirical correlation matrix towards the Gaussian prediction, rather than linear shrinkage of the covariance matrix. Shrinkage ensures the covariance is non-singular and therefore invertible, which is critical for the estimation of likelihoods and validation. We then applied a delete-2 jackknife bias correction to the diagonal components of the jackknife covariance that removed the general tendency for jackknife error estimates to be biased high. We validated internally derived covariances, which used the jackknife resampling technique, on synthetic Euclid-like lognormal catalogues. We demonstrate that DICES produces accurate, non-singular covariance estimates, with the relative error improving by 33% for the covariance and 48% for the correlation structure in comparison to jackknife estimates. These estimates can be used for highly accurate regression and inference.

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Euclid preparation. Galaxy power spectrum and bispectrum modelling

Higher-order correlation functions of the large-scale galaxy distribution offer access to information beyond that contained in standard 2-point statistics such as the power spectrum. In this work we assess this potential for the $\textit{Euclid}$ mission using synthetic catalogues of H$α$ galaxies based on the 54 $\, h^{-3} \, {\rm Gpc}^3$ Flagship I simulation, designed to reproduce the $\textit{Euclid}$ spectroscopic sample. We comprehensively validate the one-loop galaxy power spectrum and tree-level bispectrum predictions from perturbation theory in both real and redshift space. Assuming scale cuts consistent with our previous power spectrum study on the same catalogues, this modelling yields unbiased cosmological constraints for the bispectrum up to $k_{\rm max} = 0.15\,\, h \, {\rm Mpc}^{-1}$ in real space and $0.08 \, (0.1)\,\, h \, {\rm Mpc}^{-1}$ at the lowest (highest) redshift, corresponding to $z=0.9$ ($z=1.8$), for the monopole and quadrupole in redshift space using statistical uncertainties corresponding to the full simulation volume. With these scale cuts, adding bispectrum information to the power spectrum improves constraints on the amplitude of scalar perturbations and the matter density by up to 30 %, increasing the overall figure of merit for key cosmological parameters by a factor of about 2.5. Similar conclusions hold when statistical uncertainties are rescaled to a $\textit{Euclid}$-like volume, highlighting the importance of the bispectrum for fully exploiting the forthcoming $\textit{Euclid}$ data. Our analysis also provides the first detailed characterisation of the nonlinear bias model of H$α$ emitters, showing that bias relations calibrated on low-resolution \textit{N}-body simulations do not adequately describe the clustering of H$α$ galaxies at low redshift, whereas excursion-set and co-evolution relations for tidal biases remain accurate.

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Euclid Quick Data Release (Q1). AgileLens: A scalable CNN-based pipeline for strong gravitational lens identification

We present an end-to-end, iterative pipeline for efficient identification of strong galaxy--galaxy lensing systems, applied to the Euclid Q1 imaging data. Starting from VIS catalogues, we reject point sources, apply a magnitude cut (I$_E$ $\leq$ 24) on deflectors, and run a pixel-level artefact/noise filter to build 96 $\times$ 96 pix cutouts; VIS+NISP colour composites are constructed with a VIS-anchored luminance scheme that preserves VIS morphology and NISP colour contrast. A VIS-only seed classifier supplies clear positives and typical impostors, from which we curate a morphology-balanced negative set and augment scarce positives. Among the six CNNs studied initially, a modified VGG16 (GlobalAveragePooling + 256/128 dense layers with the last nine layers trainable) performs best; the training set grows from 27 seed lenses (augmented to 1809) plus 2000 negatives to a colour dataset of 30,686 images. After three rounds of iterative fine-tuning, human grading of the top 4000 candidates ranked by the final model yields 441 Grade A/B candidate lensing systems, including 311 overlapping with the existing Q1 strong-lens catalogue, and 130 additional A/B candidates (9 As and 121 Bs) not previously reported. Independently, the model recovers 740 out of 905 (81.8%) candidate Q1 lenses within its top 20,000 predictions, considering off-centred samples. Candidates span I$_E$ $\simeq$ 17--24 AB mag (median 21.3 AB mag) and are redder in Y$_E$--H$_E$ than the parent population, consistent with massive early-type deflectors. Each training iteration required a week for a small team, and the approach easily scales to future Euclid releases; future work will calibrate the selection function via lens injection, extend recall through uncertainty-aware active learning, explore multi-scale or attention-based neural networks with fast post-hoc vetters that incorporate lens models into the classification.

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Euclid preparation. Impact of redshift distribution uncertainties on the joint analysis of photometric galaxy clustering and weak gravitational lensing

One of the $\textit{Euclid}$ mission's key projects is the so-called 3$\times$2pt analysis, that is, the combination of cosmic shear, photometric galaxy clustering, and galaxy-galaxy lensing. Although $\textit{Euclid}$ has established quality requirements for the photo-$z$ accuracy needed for the weak lensing galaxy sample, no such requirements have been set for the photometric clustering sample. In this paper, we investigate the impact of redshift uncertainties on $\textit{Euclid}$'s photometric galaxy clustering analysis and its combination with weak gravitational lensing, focusing on data release 1 (DR1). In particular, we study whether having precise knowledge of the mean of the redshift distributions per bin is sufficient to avoid biases in the resulting cosmological constraints or whether accuracy in the higher-order moments of the distribution is required. We evaluate the results based on their constraining power on $w_{\mathrm{0}}$ and $w_{a}$ and define thresholds for the precision and accuracy of $\textit{Euclid}$'s redshift distribution of the photometric clustering sample. We find that the redshift distributions of the photometric clustering sample must be known at an accuracy of 0.004(1+$z$) in the mean in order to recover 80$\%$ of the constraining power in $\textit{Euclid}$'s DR1 $w_{\mathrm{0}}w_{a}$CDM 3$\times$2pt analysis. The impact of the uncertainty on the width is negligible, provided the mean redshift is constrained with sufficient accuracy. For most sources of redshift distribution error, attaining the requirement on the mean will also reduce uncertainty in the width well below the required level.

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Euclid preparation. XCII. Controlling angular systematics in the Euclid spectroscopic galaxy sample

We present the strategy used to identify and mitigate potential sources of angular systematics in the \textit{Euclid} spectroscopic galaxy survey, and we quantify their impact on galaxy clustering measurements and cosmological parameter estimation. We first surveyed the \textit{Euclid} processing pipeline to identify all evident, potential sources of systematics, and classified them into two broad classes: angular systematics, which modulate the galaxy number density across the sky, and catastrophic redshift errors, which lead to interlopers in the galaxy sample. We then used simulated spectroscopic surveys to test our ability to mitigate angular systematics by constructing a random catalogue that represents the `visibility mask' of the survey; this is a dense set of intrinsically unclustered objects, subject to the same selection effects as the data catalogue. The construction of this random catalogue relies on a detection model, which gives the probability of reliably measuring the galaxy redshift as a function of the signal-to-noise ratio (S/N) of its emission lines. We demonstrate that, in the ideal case of a perfect knowledge of the visibility mask, the galaxy power spectrum in the presence of systematics is recovered, to within sub-per cent accuracy, by convolving a theory power spectrum with a window function obtained from the random catalogue itself. In the case of only approximate knowledge of the visibility mask, we test the stability of power spectrum measurements and cosmological parameter posteriors by using perturbed versions of the random catalogue. We find that significant effects are limited to very large scales, and parameter estimation remains robust; the most impacting effects are connected to the calibration of the detection model.

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Euclid preparation. The impact of redshift interlopers on the two-point correlation function analysis

The Euclid survey aims to measure the spectroscopic redshift of emission-line galaxies by identifying the H$\,α$ line in their slitless spectra. This method is sensitive to the signal-to-noise ratio of the line, as noise fluctuations or other strong emission lines can be misidentified as H$\,α$, depending on redshift. These effects lead to catastrophic redshift errors and the inclusion of interlopers in the sample. We forecast the impact of such redshift errors on galaxy clustering measurements. In particular, we study the effect of interloper contamination on the two-point correlation function (2PCF), the growth rate of structures, and the Alcock-Paczynski (AP) parameters. We analyze 1000 synthetic spectroscopic catalogues, the EuclidLargeMocks, designed to match the area and selection function of the Data Release 1 (DR1) sample. We estimate the 2PCF of the contaminated catalogues, isolating contributions from correctly identified galaxies and from interlopers. We explore different models with increasing complexity to describe the measured 2PCF at fixed cosmology. Finally, we perform a cosmological inference and evaluate the systematic error on the inferred $fσ_8$, $α_{\parallel}$ and $α_{\perp}$ values associated with different models. Our results demonstrate that a minimal modelling approach, which only accounts for an attenuation of the clustering signal regardless of the type of contaminants, is sufficient to recover the correct values of $fσ_8$, $α_{\parallel}$, and $α_{\perp}$ at DR1. The accuracy and precision of the estimated AP parameters are largely insensitive to the presence of interlopers. The adoption of a minimal model induces a 1%-3% systematic error on the growth rate of structure estimation, depending on the redshift. However, this error remains smaller than the statistical error expected for the Euclid DR1 analysis.

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Euclid preparation. Simulated galaxy catalogues for non-standard cosmological models

Stage-IV galaxy surveys will provide the opportunity to test cosmological models and the underlying theory of gravity with unparalleled precision. In this context, it is crucial for the Euclid mission to leverage its spectroscopic and photometric probes to systematically investigate and incorporate non-standard cosmological models, including modified gravity, alternative dark energy scenarios, massive neutrinos, and primordial non-Gaussianity. We produce and release publicly simulated galaxy catalogues from a broad suite of non-standard cosmological simulations, which we processed through a model-independent analytical pipeline, making use of Rockstar for halo identification, and a modified version of the SciPic library for the galaxy-halo connection using the halo occupation distribution framework. We investigate their galaxy-clustering characteristics via the multipoles of the 2PCF in redshift space and VDG, a highly performant model for galaxy clustering. Across a wide range of models, the linear growth rate multiplied by the matter density within spheres of radius 12,Mpc, fs12, exhibits a notable robustness to the choice of cosmological template. Compared to previous works, our study extends this result to numerous scenarios with markedly distinct gravitational or dark energy dynamics. We find that the most of the scatter in cosmological parameter inference already appears when using the cosmological model of the simulations as templates. Using a `wrong' template can also introduce an additional scatter, although with smaller amplitude. Often, we find deviations much larger than error bars, meaning that the Gaussian approximation for the covariance might need to be further studied. Future cosmological investigations must broaden their scope to include a diverse array of non-standard theoretical frameworks, extending beyond LCDM and rudimentary dynamic dark energy models.

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Euclid: The linear-construction covariance and cosmology

We study the properties of galaxy cluster 2-point correlation function covariance matrices estimated using the linear-construction (LC) method, which is computationally up to 20 times faster than the standard sample-covariance method. Our goal is to assess how well the LC method performs in cosmological parameter estimation compared to the sample covariance. We use a set of 1000 mock dark matter halo catalogues to compute both the LC-covariance and the sample-covariance estimates in four redshift shells. These numerical matrices are used to fit a theoretical four-parameter model for the covariance. We then use the two fitted covariance models in a likelihood function to estimate two cosmological parameters - the matter density parameter $Ω_{\rm m}$ and the amplitude of the matter density fluctuations $σ_8$ - from the simulated mock catalogues. The purpose of this is to validate the LC-covariance-based model against the sample-covariance model. The catalogues were simulated assuming the spatially flat $Λ$CDM cosmology, with $Ω_{\rm m} = 0.30711$ and $σ_8=0.8288$. We find that the parameter posteriors obtained using the sample- and LC-covariance models agree well with each other and with the simulation cosmology. The two pairs of marginalized constraints are $Ω_{\rm m} = 0.307 \pm 0.003$ and $σ_8 = 0.826\pm 0.009$ (sample covariance), and $Ω_{\rm m} = 0.308 \pm 0.003$ and $σ_8 = 0.825 \pm 0.009$ (LC covariance). The posterior widths are the same, and the difference in the median values is less than $0.16\,σ$ for both parameters.

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Euclid preparation. Galaxy power spectrum modelling in redshift space

Accurate modelling of redshift-space distortions (RSD) is essential for maximizing the cosmological information extracted from large galaxy redshift surveys. In preparation for the forthcoming analysis of the Euclid spectroscopic data, we investigate three approaches to modelling RSD effects on the power spectrum multipoles of mock H$α$ emission line galaxies. We focus on two one-loop perturbation theory models -- the effective field theory (EFT) and velocity difference generator (${\rm VDG_ \infty}$) -- which differ in their treatment of the real-to-redshift space mapping on small scales, and a third approach, the BACCO emulator, which adopts a hybrid strategy combining perturbation theory with high-resolution N-body simulations. We assess the ability of these models to recover key cosmological parameters, including the expansion rate $h$, the cold dark matter density parameter $ω_{\rm c}$, and the scalar amplitude $A_{\rm s}$, across four redshift bins spanning $0.9 \leq z \leq 1.8$. In each bin, we find that ${\rm VDG_ \infty}$ and BACCO outperform the EFT model across all scales up to $k_{max} \lesssim 0.35 h\,Mpc^{-1} $. While BACCO saturates in constraining power at intermediate scales and higher redshift, the ${\rm VDG_ \infty}$ model continues to improve parameter constraints beyond $k_{max} \gtrsim 0.30 h\,Mpc^{-1}$. The EFT model, although robust on large scales, exhibits significant parameter biases for $k_{max} \gtrsim 0.25 h\,Mpc^{-1}$, limiting its applicability to Euclid-like H$α$ samples. Among the full perturbation theory-based models, the enhanced treatment of small-scale RSD effects in ${\rm VDG_ \infty}$ improves cosmological parameter constraints by up to a factor of two.

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Euclid Quick Data Release (Q1). LEMON -- Lens Modelling with Neural networks. Automated and fast modelling of Euclid gravitational lenses with a singular isothermal ellipsoid mass profile

The Euclid mission aims to survey around 14000 deg^{2} of extragalactic sky, providing around 10^{5} gravitational lens images. Modelling of gravitational lenses is fundamental to estimate the total mass of the lens galaxy, along with its dark matter content. Traditional modelling of gravitational lenses is computationally intensive and requires manual input. In this paper, we use a Bayesian neural network, LEns MOdelling with Neural networks (LEMON), to model Euclid gravitational lenses with a singular isothermal ellipsoid mass profile. Our method estimates key lens mass profile parameters, such as the Einstein radius, while also predicting the light parameters of foreground galaxies and their uncertainties. We validate LEMON's performance on both mock Euclid datasets, real lenses observed with Hubble Space Telescope (HST), and real Euclid lenses, demonstrating the ability of LEMON to predict parameters of both simulated and real lenses. Results show promising accuracy and reliability in predicting the Einstein radius, mass and light ellipticities, effective radius, Sérsic index, lens magnitude, and unlensed source position for simulated lens galaxies. The application to real data, including the latest Quick Release 1 strong lens candidates, provides encouraging results in the recovery of the parameters for real lenses. We also verified that LEMON has the potential to accelerate traditional modelling methods, by giving to the classical optimiser the LEMON predictions as starting points, resulting in a speed-up of up to 26 times the original time needed to model a sample of gravitational lenses, a result that would be impossible with randomly initialised guesses. This work represents a significant step towards efficient, automated gravitational lens modelling, which is crucial for handling the large data volumes expected from Euclid.

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Euclid preparation: LXXXVII. Non-Gaussianity of 2-point statistics likelihood: Precise analysis of the matter power spectrum distribution

We investigate the non-Gaussian features in the distribution of the matter power spectrum multipoles. Using the COVMOS method, we generate 100\,000 mock realisations of dark matter density fields in both real and redshift space across multiple redshifts and cosmological models. We derive an analytical framework linking the non-Gaussianity of the power spectrum distribution to higher-order statistics of the density field, including the trispectrum and pentaspectrum. We explore the effect of redshift-space distortions, the geometry of the survey, the Fourier binning, the integral constraint, and the shot noise on the skewness of the distribution of the power spectrum measurements. Our results demonstrate that the likelihood of the estimated matter power spectrum deviates significantly from a Gaussian assumption on nonlinear scales, particularly at low redshift. This departure is primarily driven by the pentaspectrum contribution, which dominates over the trispectrum at intermediate scales. We also examine the impact of the finiteness of the survey geometry in the context of the Euclid mission and find that both the shape of the survey and the integral constraint amplify the skewness.

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Euclid: An emulator for baryonic effects on the matter bispectrum

Understanding the impact of baryonic processes such as star formation and active galactic nuclei (AGN) feedback on matter clustering is crucial to ensure precise and unbiased cosmological inference. Most theoretical models of baryonic effects to date focus on two-point statistics, neglecting higher-order contributions. This work develops a fast and accurate emulator for baryonic effects on the matter bispectrum, a key non-Gaussian statistic in the nonlinear regime. We employ high-resolution $N$-body simulations from the BACCO suite and apply a combination of cutting-edge techniques such as cosmology scaling and baryonification to efficiently span a large cosmological and astrophysical parameter space. A deep neural network is trained to emulate baryonic effects on the matter bispectrum measured in simulations, capturing modifications across various scales and redshifts relevant to Euclid. We validate the emulator accuracy and robustness using an analysis of \Euclid mock data, employing predictions from the state-of-the-art FLAMINGO hydrodynamical simulations. The emulator reproduces baryonic suppression in the bispectrum to better than 2$\%$ for the $68\%$ percentile across most triangle configurations for $k \in [0.01, 20]\,\mathrm{i}h\mathrm{Mpc}^{-1}$ and ensures consistency between cosmological posteriors inferred from second- and third-order weak lensing statistics. These results demonstrate that our emulator meets the high-precision requirements of the Euclid mission for at least the first data release and provides reliable forecasts of the cosmological information contained in the small-scale matter bispectrum. This underscores the potential of emulation techniques to bridge the gap between complex baryonic physics and observational data, maximising the scientific output of Euclid.

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Euclid: Galaxy SED reconstruction in the PHZ processing function: impact on the PSF and the role of medium-band filters

Weak lensing surveys require accurate correction for the point spread function (PSF) when measuring galaxy shapes. For a diffraction-limited PSF, as arises in space-based missions, this correction depends on each galaxy SED. In the Euclid mission, galaxy SED reconstruction, a tasks of the photometric-redshift processing function (PHZ PF), relies on broad- and medium-band ancillary photometry. The limited wavelength sampling of the Euclid VIS passband and signal-to-noise ratio may affect the reconstruction accuracy and translate into biases in the weak lensing measurements. In this study, we present the methodology, which is employed in the Euclid PHZ PF, for reconstructing galaxy SEDs at 55 wavelengths, sampling the VIS passband every 10 nm, and we assess whether it fulfils the accuracy requirements imposed on the Euclid PSF model. We employ both physics- and data-driven methods, focusing on a new approach of template-based flux correction and Gaussian processes, and we introduce an SED metric whose bias propagates into PSF quadrupole moment errors. Our findings demonstrate that Gaussian processes and template fitting meet the requirements only in specific, but complementary, redshift intervals. We therefore propose a hybrid approach, which leverages both methods. This solution proves to be effective in meeting the Euclid accuracy requirements for most of the redshift range of the survey. Finally, we investigate the impact on the SED reconstruction of a new set of 16 evenly-spaced medium-band filters for the Subaru telescope, providing quasi-spectroscopic coverage of the VIS passband. This study shows promising results, ensuring accurate SED reconstruction and meeting the mission PSF requirements. This work thus provides not only the methodological foundation of galaxy SED reconstruction in the Euclid PHZ PF, but also a roadmap for future improvements using a new medium-band survey.

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Euclid preparation. Calibrated intrinsic galaxy alignments in the Euclid Flagship simulation

Intrinsic alignments of galaxies are potentially a major contaminant of cosmological analyses of weak gravitational lensing. We construct a semi-analytic model of galaxy ellipticities and alignments in the \Euclid Flagship simulation to predict this contamination in Euclid's weak lensing observations. Galaxy shapes and orientations are determined by the corresponding properties of the host haloes in the underlying $N$-body simulation, as well as the relative positions of galaxies within their halo. Alignment strengths are moderated via stochastic misalignments, separately for central and satellite galaxies and conditional on the galaxy's redshift, luminosity, and rest-frame colour. The resulting model is calibrated against galaxy ellipticity statistics from the COSMOS Survey, selected alignment measurements based on Sloan Digital Sky Survey samples, and galaxy orientations extracted from the Horizon-AGN hydrodynamic simulation at redshift $z=1$. The best-fit model has a total of 12 alignment parameters and generally reproduces the calibration data sets well within the $1σ$ statistical uncertainties of the observations and the \flagship simulation, with notable exceptions for the most luminous sub-samples on small physical scales. The statistical power of the calibration data and the volume of the single \flagship realisation are still too small to provide informative prior ranges for intrinsic alignment amplitudes in relevant galaxy samples. As a first application, we predict that \Euclid end-of-mission tomographic weak gravitational lensing two-point statistics are modified by up to order $10\,\%$ due to intrinsic alignments.

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