arXiv subjects

I. Tutusaus

Publications and source records attributed to I. Tutusaus.

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arXiv2022

Dark Energy Survey Year 3 Results: Cosmology from Cosmic Shear and Robustness to Modeling Uncertainty

This work and its companion paper, Amon et al. (2021), present cosmic shear measurements and cosmological constraints from over 100 million source galaxies in the Dark Energy Survey (DES) Year 3 data. We constrain the lensing amplitude parameter $S_8\equivσ_8\sqrt{Ω_\textrm{m}/0.3}$ at the 3% level in $Λ$CDM: $S_8=0.759^{+0.025}_{-0.023}$ (68% CL). Our constraint is at the 2% level when using angular scale cuts that are optimized for the $Λ$CDM analysis: $S_8=0.772^{+0.018}_{-0.017}$ (68% CL). With cosmic shear alone, we find no statistically significant constraint on the dark energy equation-of-state parameter at our present statistical power. We carry out our analysis blind, and compare our measurement with constraints from two other contemporary weak-lensing experiments: the Kilo-Degree Survey (KiDS) and Hyper-Suprime Camera Subaru Strategic Program (HSC). We additionally quantify the agreement between our data and external constraints from the Cosmic Microwave Background (CMB). Our DES Y3 result under the assumption of $Λ$CDM is found to be in statistical agreement with Planck 2018, although favors a lower $S_8$ than the CMB-inferred value by $2.3σ$ (a $p$-value of 0.02). This paper explores the robustness of these cosmic shear results to modeling of intrinsic alignments, the matter power spectrum and baryonic physics. We additionally explore the statistical preference of our data for intrinsic alignment models of different complexity. The fiducial cosmic shear model is tested using synthetic data, and we report no biases greater than 0.3$σ$ in the plane of $S_8\timesΩ_\textrm{m}$ caused by uncertainties in the theoretical models.

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arXiv2021

The DES view of the Eridanus supervoid and the CMB Cold Spot

The Cold Spot is a puzzling large-scale feature in the Cosmic Microwave Background temperature maps and its origin has been subject to active debate. As an important foreground structure at low redshift, the Eridanus supervoid was recently detected, but it was subsequently determined that, assuming the standard $Λ$CDM model, only about 10-20$\%$ of the observed temperature depression can be accounted for via its Integrated Sachs-Wolfe imprint. However, $R\gtrsim100~h^{-1}\mathrm{Mpc}$ supervoids elsewhere in the sky have shown ISW imprints $A_{\mathrm{ISW}}\approx5.2\pm1.6$ times stronger than expected from $Λ$CDM ($A_{\mathrm{ISW}}=1$), which warrants further inspection. Using the Year-3 redMaGiC catalogue of luminous red galaxies from the Dark Energy Survey, here we confirm the detection of the Eridanus supervoid as a significant under-density in the Cold Spot's direction at $z<0.2$. We also show, with $\mathrm{S/N}\gtrsim5$ significance, that the Eridanus supervoid appears as the most prominent large-scale under-density in the dark matter mass maps that we reconstructed from DES Year-3 gravitational lensing data. While we report no significant anomalies, an interesting aspect is that the amplitude of the lensing signal from the Eridanus supervoid at the Cold Spot centre is about $30\%$ lower than expected from similar peaks found in N-body simulations based on the standard $Λ$CDM model with parameters $Ω_{\rm m} = 0.279$ and $σ_8 = 0.82$. Overall, our results confirm the causal relation between these individually rare structures in the cosmic web and in the CMB, motivating more detailed future surveys in the Cold Spot region.

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arXiv2021

Dark Energy Survey Year 3 Results: Galaxy mock catalogs for BAO analysis

The calibration and validation of scientific analysis in simulations is a fundamental tool to ensure unbiased and robust results in observational cosmology. In particular, mock galaxy catalogs are a crucial resource to achieve these goals in the measurement of baryon acoustic oscillation (BAO) in the clustering of galaxies. Here we present a set of 1952 galaxy mock catalogs designed to mimic the Dark Energy Survey (DES) Year 3 BAO sample over its full photometric redshift range $0.6<z_{\rm photo}<1.1$. The mocks are based upon 488 ICE-COLA fast $N$-body simulations of full-sky light cones and were created by populating halos with galaxies, using a hybrid halo occupation distribution - halo abundance matching model. This model has ten free parameters, which were determined, for the first time, using an automatic likelihood minimization procedure. We also introduced a novel technique to assign photometric redshift for simulated galaxies, following a two-dimensional probability distribution with VIMOS Public Extragalactic Redshift Survey (VIPERS) data. The calibration was designed to match the observed abundance of galaxies as a function of photometric redshift, the distribution of photometric redshift errors, and the clustering amplitude on scales smaller than those used for BAO measurements. An exhaustive analysis was done to ensure that the mocks reproduce the input properties. Finally, mocks were tested by comparing the angular correlation function $w(θ)$, angular power spectrum $C_\ell$, and projected clustering $ξ_p(r_\perp)$ to theoretical predictions and data. The impact of volume replication in the estimate of the covariance is also investigated. The success in accurately reproducing the photometric redshift uncertainties and the galaxy clustering as a function of redshift render this mock creation pipeline as a benchmark for future analyses of photometric galaxy surveys.

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arXiv2021

Dark Energy Survey Year 3 results: curved-sky weak lensing mass map reconstruction

We present reconstructed convergence maps, \textit{mass maps}, from the Dark Energy Survey (DES) third year (Y3) weak gravitational lensing data set. The mass maps are weighted projections of the density field (primarily dark matter) in the foreground of the observed galaxies. We use four reconstruction methods, each is a \textit{maximum a posteriori} estimate with a different model for the prior probability of the map: Kaiser-Squires, null B-mode prior, Gaussian prior, and a sparsity prior. All methods are implemented on the celestial sphere to accommodate the large sky coverage of the DES Y3 data. We compare the methods using realistic $Λ$CDM simulations with mock data that are closely matched to the DES Y3 data. We quantify the performance of the methods at the map level and then apply the reconstruction methods to the DES Y3 data, performing tests for systematic error effects. The maps are compared with optical foreground cosmic-web structures and are used to evaluate the lensing signal from cosmic-void profiles. The recovered dark matter map covers the largest sky fraction of any galaxy weak lensing map to date.

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arXiv2021

Dark Energy Survey Year 3 results: Cosmology with peaks using an emulator approach

We constrain the matter density $Ω_{\mathrm{m}}$ and the amplitude of density fluctuations $σ_8$ within the $Λ$CDM cosmological model with shear peak statistics and angular convergence power spectra using mass maps constructed from the first three years of data of the Dark Energy Survey (DES Y3). We use tomographic shear peak statistics, including cross-peaks: peak counts calculated on maps created by taking a harmonic space product of the convergence of two tomographic redshift bins. Our analysis follows a forward-modelling scheme to create a likelihood of these statistics using N-body simulations, using a Gaussian process emulator. We include the following lensing systematics: multiplicative shear bias, photometric redshift uncertainty, and galaxy intrinsic alignment. Stringent scale cuts are applied to avoid biases from unmodelled baryonic physics. We find that the additional non-Gaussian information leads to a tightening of the constraints on the structure growth parameter yielding $S_8~\equiv~σ_8\sqrt{Ω_{\mathrm{m}}/0.3}~=~0.797_{-0.013}^{+0.015}$ (68% confidence limits), with a precision of 1.8%, an improvement of ~38% compared to the angular power spectra only case. The results obtained with the angular power spectra and peak counts are found to be in agreement with each other and no significant difference in $S_8$ is recorded. We find a mild tension of $1.5 \thinspace σ$ between our study and the results from Planck 2018, with our analysis yielding a lower $S_8$. Furthermore, we observe that the combination of angular power spectra and tomographic peak counts breaks the degeneracy between galaxy intrinsic alignment $A_{\mathrm{IA}}$ and $S_8$, improving cosmological constraints. We run a suite of tests concluding that our results are robust and consistent with the results from other studies using DES Y3 data.

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arXiv2021

$Euclid$ preparation: XV. Forecasting cosmological constraints for the $Euclid$ and CMB joint analysis

The combination and cross-correlation of the upcoming $Euclid$ data with cosmic microwave background (CMB) measurements is a source of great expectation since it will provide the largest lever arm of epochs, ranging from recombination to structure formation across the entire past light cone. In this work, we present forecasts for the joint analysis of $Euclid$ and CMB data on the cosmological parameters of the standard cosmological model and some of its extensions. This work expands and complements the recently published forecasts based on $Euclid$-specific probes, namely galaxy clustering, weak lensing, and their cross-correlation. With some assumptions on the specifications of current and future CMB experiments, the predicted constraints are obtained from both a standard Fisher formalism and a posterior-fitting approach based on actual CMB data. Compared to a $Euclid$-only analysis, the addition of CMB data leads to a substantial impact on constraints for all cosmological parameters of the standard $Λ$-cold-dark-matter model, with improvements reaching up to a factor of ten. For the parameters of extended models, which include a redshift-dependent dark energy equation of state, non-zero curvature, and a phenomenological modification of gravity, improvements can be of the order of two to three, reaching higher than ten in some cases. The results highlight the crucial importance for cosmological constraints of the combination and cross-correlation of $Euclid$ probes with CMB data.

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arXiv2021

Cross-correlation of DES Y3 lensing and ACT/${\it Planck}$ thermal Sunyaev Zel'dovich Effect I: Measurements, systematics tests, and feedback model constraints

We present a tomographic measurement of the cross-correlation between thermal Sunyaev-Zeldovich (tSZ) maps from ${\it Planck}$ and the Atacama Cosmology Telescope (ACT) and weak galaxy lensing shears measured during the first three years of observations of the Dark Energy Survey (DES Y3). This correlation is sensitive to the thermal energy in baryons over a wide redshift range, and is therefore a powerful probe of astrophysical feedback. We detect the correlation at a statistical significance of $21σ$, the highest significance to date. We examine the tSZ maps for potential contaminants, including cosmic infrared background (CIB) and radio sources, finding that CIB has a substantial impact on our measurements and must be taken into account in our analysis. We use the cross-correlation measurements to test different feedback models. In particular, we model the tSZ using several different pressure profile models calibrated against hydrodynamical simulations. Our analysis marginalises over redshift uncertainties, shear calibration biases, and intrinsic alignment effects. We also marginalise over $Ω_{\rm m}$ and $σ_8$ using ${\it Planck}$ or DES priors. We find that the data prefers the model with a low amplitude of the pressure profile at small scales, compatible with a scenario with strong AGN feedback and ejection of gas from the inner part of the halos. When using a more flexible model for the shear profile, constraints are weaker, and the data cannot discriminate between different baryonic prescriptions.

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arXiv2021

Euclid: Forecasts for $k$-cut $3 \times 2$ Point Statistics

Modelling uncertainties at small scales, i.e. high $k$ in the power spectrum $P(k)$, due to baryonic feedback, nonlinear structure growth and the fact that galaxies are biased tracers poses a significant obstacle to fully leverage the constraining power of the {\it Euclid} wide-field survey. $k$-cut cosmic shear has recently been proposed as a method to optimally remove sensitivity to these scales while preserving usable information. In this paper we generalise the $k$-cut cosmic shear formalism to $3 \times 2$ point statistics and estimate the loss of information for different $k$-cuts in a $3 \times 2$ point analysis of the {\it Euclid} data. Extending the Fisher matrix analysis of~\citet{blanchard2019euclid}, we assess the degradation in constraining power for different $k$-cuts. We work in the idealised case and assume the galaxy bias is linear, the covariance is Gaussian, while neglecting uncertainties due to photo-z errors and baryonic feedback. We find that taking a $k$-cut at $2.6 \ h \ {\rm Mpc} ^{-1}$ yields a dark energy Figure of Merit (FOM) of 1018. This is comparable to taking a weak lensing cut at $\ell = 5000$ and a galaxy clustering and galaxy-galaxy lensing cut at $\ell = 3000$ in a traditional $3 \times 2$ point analysis. We also find that the fraction of the observed galaxies used in the photometric clustering part of the analysis is one of the main drivers of the FOM. Removing $50 \% \ (90 \%)$ of the clustering galaxies decreases the FOM by $19 \% \ (62 \%)$. Given that the FOM depends so heavily on the fraction of galaxies used in the clustering analysis, extensive efforts should be made to handle the real-world systematics present when extending the analysis beyond the luminous red galaxy (LRG) sample.

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arXiv2021

Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation

This paper details the modeling pipeline and validates the baseline analysis choices of the DES Year 3 joint analysis of galaxy clustering and weak lensing (a so-called "3$\times$2pt" analysis). These analysis choices include the specific combination of cosmological probes, priors on cosmological and systematics parameters, model parameterizations for systematic effects and related approximations, and angular scales where the model assumptions are validated. We run a large number of simulated likelihood analyses using synthetic data vectors to test the robustness of our baseline analysis. We demonstrate that the DES Year 3 modeling pipeline, including the calibrated scale cuts, is sufficiently accurate relative to the constraining power of the DES Year 3 analyses. Our systematics mitigation strategy accounts for astrophysical systematics, such as galaxy bias, intrinsic alignments, source and lens magnification, baryonic effects, and source clustering, as well as for uncertainties in modeling the matter power spectrum, reduced shear, and estimator effects. We further demonstrate excellent agreement between two independently-developed modeling pipelines, and thus rule out any residual uncertainties due to the numerical implementation.

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arXiv2021

Euclid: constraining dark energy coupled to electromagnetism using astrophysical and laboratory data

In physically realistic scalar-field based dynamical dark energy models (including, e.g., quintessence) one naturally expects the scalar field to couple to the rest of the model's degrees of freedom. In particular, a coupling to the electromagnetic sector leads to a time (redshift) dependence of the fine-structure constant and a violation of the Weak Equivalence Principle. Here we extend the previous Euclid forecast constraints on dark energy models to this enlarged (but physically more realistic) parameter space, and forecast how well Euclid, together with high-resolution spectroscopic data and local experiments, can constrain these models. Our analysis combines simulated Euclid data products with astrophysical measurements of the fine-structure constant, $α$, and local experimental constraints, and includes both parametric and non-parametric methods. For the astrophysical measurements of $α$ we consider both the currently available data and a simulated dataset representative of Extremely Large Telescope measurements and expected to be available in the 2030s. Our parametric analysis shows that in the latter case the inclusion of astrophysical and local data improves the Euclid dark energy figure of merit by between $8\%$ and $26\%$, depending on the correct fiducial model, with the improvements being larger in the null case where the fiducial coupling to the electromagnetic sector is vanishing. These improvements would be smaller with the current astrophysical data. Moreover, we illustrate how a genetic algorithms based reconstruction provides a null test for the presence of the coupling. Our results highlight the importance of complementing surveys like Euclid with external data products, in order to accurately test the wider parameter spaces of physically motivated paradigms.

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arXiv2021

Euclid preparation: XII. Optimizing the photometric sample of the Euclid survey for galaxy clustering and galaxy-galaxy lensing analyses

The accuracy of photometric redshifts (photo-zs) particularly affects the results of the analyses of galaxy clustering with photometrically-selected galaxies (GCph) and weak lensing. In the next decade, space missions like Euclid will collect photometric measurements for millions of galaxies. These data should be complemented with upcoming ground-based observations to derive precise and accurate photo-zs. In this paper, we explore how the tomographic redshift binning and depth of ground-based observations will affect the cosmological constraints expected from Euclid. We focus on GCph and extend the study to include galaxy-galaxy lensing (GGL). We add a layer of complexity to the analysis by simulating several realistic photo-z distributions based on the Euclid Consortium Flagship simulation and using a machine learning photo-z algorithm. We use the Fisher matrix formalism and these galaxy samples to study the cosmological constraining power as a function of redshift binning, survey depth, and photo-z accuracy. We find that bins with equal width in redshift provide a higher Figure of Merit (FoM) than equipopulated bins and that increasing the number of redshift bins from 10 to 13 improves the FoM by 35% and 15% for GCph and its combination with GGL, respectively. For GCph, an increase of the survey depth provides a higher FoM. But the addition of faint galaxies beyond the limit of the spectroscopic training data decreases the FoM due to the spurious photo-zs. When combining both probes, the number density of the sample, which is set by the survey depth, is the main factor driving the variations in the FoM. We conclude that there is more information that can be extracted beyond the nominal 10 tomographic redshift bins of Euclid and that we should be cautious when adding faint galaxies into our sample, since they can degrade the cosmological constraints.

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arXiv2021

Euclid: Forecast constraints on the cosmic distance duality relation with complementary external probes

In metric theories of gravity with photon number conservation, the luminosity and angular diameter distances are related via the Etherington relation, also known as the distance-duality relation (DDR). A violation of this relation would rule out the standard cosmological paradigm and point at the presence of new physics. We quantify the ability of Euclid, in combination with contemporary surveys, to improve the current constraints on deviations from the DDR in the redshift range $0<z<1.6$. We start by an analysis of the latest available data, improving previously reported constraints by a factor of 2.5. We then present a detailed analysis of simulated Euclid and external data products, using both standard parametric methods (relying on phenomenological descriptions of possible DDR violations) and a machine learning reconstruction using Genetic Algorithms. We find that for parametric methods Euclid can (in combination with external probes) improve current constraints by approximately a factor of six, while for non-parametric methods Euclid can improve current constraints by a factor of three. Our results highlight the importance of surveys like Euclid in accurately testing the pillars of the current cosmological paradigm and constraining physics beyond the standard cosmological model.

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arXiv2020

Euclid preparation: VII. Forecast validation for Euclid cosmological probes

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. Estimation of the expected performance of the experiment, in terms of predicted constraints on cosmological parameters, has so far relied on different methodologies and numerical implementations, developed for different observational probes and for their combination. In this paper we present validated forecasts, that combine both theoretical and observational expertise for different cosmological probes. This is presented to provide the community with reliable numerical codes and methods for Euclid cosmological forecasts. We describe in detail the methodology adopted for Fisher matrix forecasts, applied to galaxy clustering, weak lensing and their combination. We estimate 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 that can be used by the reader to validate their own codes if required. We present new cosmological forecasts for Euclid. We find that results depend on the specific cosmological model and remaining freedom in each setup, i.e. flat or non-flat spatial cosmologies, or different cuts at nonlinear scales. The validated numerical implementations can now be reliably used for any setup. We present results for an optimistic and a pessimistic choice of such 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.

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arXiv2020

Euclid: impact of nonlinear prescriptions on cosmological parameter estimation from weak lensing cosmic shear

Upcoming surveys will map the growth of large-scale structure with unprecented precision, improving our understanding of the dark sector of the Universe. Unfortunately, much of the cosmological information is encoded by the small scales, where the clustering of dark matter and the effects of astrophysical feedback processes are not fully understood. This can bias the estimates of cosmological parameters, which we study here for a joint analysis of mock Euclid cosmic shear and Planck cosmic microwave background data. We use different implementations for the modelling of the signal on small scales and find that they result in significantly different predictions. Moreover, the different nonlinear corrections lead to biased parameter estimates, especially when the analysis is extended into the highly nonlinear regime, with both the Hubble constant, $H_0$, and the clustering amplitude, $σ_8$, affected the most. Improvements in the modelling of nonlinear scales will therefore be needed if we are to resolve the current tension with more and better data. For a given prescription for the nonlinear power spectrum, using different corrections for baryon physics does not significantly impact the precision of Euclid, but neglecting these correction does lead to large biases in the cosmological parameters. In order to extract precise and unbiased constraints on cosmological parameters from Euclid cosmic shear data, it is therefore essential to improve the accuracy of the recipes that account for nonlinear structure formation, as well as the modelling of the impact of astrophysical processes that redistribute the baryons.

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arXiv2020

Spherical collapse in Generalized Dark Matter models

The influence of considering a generalized dark matter (GDM) model, which allows for a non-pressure-less dark matter and a non-vanishing sound speed in the non-linear spherical collapse model is discussed for the Einstein-de Sitter-like (EdSGDM) and $Λ$GDM models. By assuming that the vacuum component responsible for the accelerated expansion of the Universe is not clustering and therefore behaving similarly to the cosmological constant $Λ$, we show how the change in the GDM characteristic parameters affects the linear density threshold for collapse of the non-relativistic component ($δ_{\rm c}$) and its virial overdensity ($Δ_{\rm V}$). We found that the generalized dark matter equation of state parameter $w_{\rm gdm}$ is responsible for lower values of the linear overdensity parameter as compared to the standard spherical collapse model and that this effect is much stronger than the one induced by a change in the generalized dark matter sound speed $c^2_{\rm s, gdm}$. We also found that the virial overdensity is only slightly affected and mostly sensitive to the generalized dark matter equation of state parameter $w_{\rm gdm}$. These effects could be relatively enhanced for lower values of the matter density. Finally, we found that the effects of the additional physics on $δ_{\rm c}$ and $Δ_{\rm V}$, when translated to non-linear observables such as the halo mass function, induce an overall deviation of about 40\% with respect to the standard $Λ$CDM model at late times for high mass objects. However, within the current linear constraints for $c^2_{\rm s, gdm}$ and $w_{\rm gdm}$, we found that these changes are the consequence of properly taking into account the correct linear matter power spectrum for the GDM model while the effects coming from modifications in the spherical collapse model remain negligible.

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arXiv2020

Validating the Fisher approach for stage IV spectroscopic surveys

In recent years forecasting activities have become a very important tool for designing and optimising large scale structure surveys. To predict the performance of such surveys, the Fisher matrix formalism is frequently used as a fast and easy way to compute constraints on cosmological parameters. Among them lies the study of the properties of dark energy which is one of the main goals in modern cosmology. As so, a metric for the power of a survey to constrain dark energy is provided by the Figure of merit (FoM). This is defined as the inverse of the surface contour given by the joint variance of the dark energy equation of state parameters $\{w_0,w_a\}$ in the Chevallier-Polarski-Linder parameterisation, which can be evaluated from the covariance matrix of the parameters. This covariance matrix is obtained as the inverse of the Fisher matrix. Inversion of an ill-conditioned matrix can result in large errors on the covariance coefficients if the elements of the Fisher matrix have been estimated with insufficient precision. The conditioning number is a metric providing a mathematical lower limit to the required precision for a reliable inversion, but it is often too stringent in practice for Fisher matrices with size larger than $2\times2$. In this paper we propose a general numerical method to guarantee a certain precision on the inferred constraints, like the FoM. It consists on randomly vibrating (perturbing) the Fisher matrix elements with Gaussian perturbations of a given amplitude, and then evaluating the maximum amplitude that keeps the FoM within the chosen precision. The steps used in the numerical derivatives and integrals involved in the calculation of the Fisher matrix elements can then be chosen accordingly in order to keep the precision of the Fisher matrix elements below this maximum amplitude...

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arXiv2020

Euclid: The importance of galaxy clustering and weak lensing cross-correlations within the photometric Euclid survey

The data from the Euclid mission will enable the measurement of the photometric redshifts, angular positions, and weak lensing shapes for over a billion galaxies. This large dataset will allow for cosmological analyses using the angular clustering of galaxies and cosmic shear. The cross-correlation (XC) between these probes can tighten constraints and it is therefore important to quantify their impact for Euclid. In this study we carefully quantify the impact of XC not only on the final parameter constraints for different cosmological models, but also on the nuisance parameters. In particular, we aim at understanding the amount of additional information that XC can provide for parameters encoding systematic effects, such as galaxy bias or intrinsic alignments (IA). We follow the formalism presented in Euclid Collaboration: Blanchard et al. (2019) and make use of the codes validated therein. We show that XC improves the dark energy Figure of Merit (FoM) by a factor $\sim 5$, whilst it also reduces the uncertainties on galaxy bias by $\sim 17\%$ and the uncertainties on IA by a factor $\sim 4$. We observe that the role of XC on the final parameter constraints is qualitatively the same irrespective of the galaxy bias model used. We also show that XC can help in distinguishing between different IA models, and that if IA terms are neglected then this can lead to significant biases on the cosmological parameters. We find that the XC terms are necessary to extract the full information content from the data in future analyses. They help in better constraining the cosmological model, and lead to a better understanding of the systematic effects that contaminate these probes. Furthermore, we find that XC helps in constraining the mean of the photometric-redshift distributions, but it requires a more precise knowledge of this mean in order not to degrade the final FoM. [Abridged]

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arXiv2020

Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments

Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant.

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