Euclid: Covariance of weak lensing pseudo-$C_{\ell }$ estimates. Calculation, comparison to simulations, and dependence on survey geometry

Abstract

An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-$C_{\ell }$ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding good agreement. We find that as a more extreme sky cut is applied, a corresponding increase in both Gaussian off-diagonal covariance and non-Gaussian super-sample covariance is observed in both theory and simulations, in accordance with expectations. Studying the different contributions to the covariance in detail, we find that the Gaussian covariance dominates along the main diagonal and the closest off-diagonals, but further away from the main diagonal the super-sample covariance is dominant. Forming mock constraints in parameters describing matter clustering and dark energy, we find that neglecting non-Gaussian contributions to the covariance can lead to underestimating the true size of confidence regions by up to 70 per cent. The dominant non-Gaussian covariance component is the super-sample covariance, but neglecting the smaller connected non-Gaussian covariance can still lead to the underestimation of uncertainties by 10--20 per cent. A real cosmological analysis will require marginalisation over many nuisance parameters, which will decrease the relative importance of all cosmological contributions to the covariance, so these values should be taken as upper limits on the importance of each component.

arXiv comment15 pages, 8 figures; matches version accepted by A&A; code available at https://github.com/robinupham/shear_pcl_cov

References in corpus (58)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Efficient Computation of CMB anisotropies in closed FRW models
• LSST: from Science Drivers to Reference Design and Anticipated Data Products
• Stable clustering, the halo model and nonlinear cosmological power spectra
• Halo Models of Large Scale Structure
• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data
• CMB power spectrum parameter degeneracies in the era of precision cosmology
• A unified pseudo-$C_{\ell }$ framework
• CosmoSIS: modular cosmological parameter estimation
• Cosmology with Phase 1 of the Square Kilometre Array; Red Book 2018: Technical specifications and performance forecasts
• Power Spectrum Super-Sample Covariance
• CosmoLike - Cosmological Likelihood Analyses for Photometric Galaxy Surveys
• Parameter inference with estimated covariance matrices
• Analysis of two-point statistics of cosmic shear: I. Estimators and covariances
• Myths and Truths Concerning Estimation of Power Spectra
• Super-Sample Covariance in Simulations
• Power Spectrum Covariance of Weak Gravitational Lensing
• The Impact of Non-Gaussian Errors on Weak Lensing Surveys
• Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments
• On measuring the covariance matrix of the nonlinear power spectrum from simulations
• Dark Energy Survey Year 1 Results: Multi-Probe Methodology and Simulated Likelihood Analyses
• CMB temperature and polarisation pseudo-Cl estimators and covariances
• Position-dependent power spectrum of the large-scale structure: a novel method to measure the squeezed-limit bispectrum
• Cosmic shear covariance: The log-normal approximation
• Dark Energy Survey Year 3 Results: Covariance Modelling and its Impact on Parameter Estimation and Quality of Fit
• 2D-FFTLog: Efficient computation of real space covariance matrices for galaxy clustering and weak lensing
• Analysis of two-point statistics of cosmic shear: III. Covariances of shear measures made easy
• Baryonic effects for weak lensing. Part I. Power spectrum and covariance matrix
• Cosmology Intertwined I: Perspectives for the Next Decade
• Cosmological Simulations for Combined-Probe Analyses: Covariance and Neighbour-Exclusion Bias
• Error analysis of quadratic power spectrum estimates for CMB polarization: sampling covariance
• The angle-averaged squeezed limit of nonlinear matter N-point functions
• Simulations of Weak Gravitational Lensing - II : Including Finite Support Effects in Cosmic Shear Covariance Matrices
• Accurate cosmic shear errors: do we need ensembles of simulations?
• SKA Weak Lensing I: Cosmological Forecasts and the Power of Radio-Optical Cross-Correlations
• Complete super-sample lensing covariance in the response approach
• Disconnected pseudo-$C_{\ell }$ covariances for projected large-scale structure data
• Cosmic Shear Covariance Matrix in $w$CDM: Cosmology Matters
• Cosmic shear power spectra in practice
• Responses in Large-Scale Structure
• Simulations of Wide-Field Weak Lensing Surveys II: Covariance Matrix of Real Space Correlation Functions
• Probing cosmology with weak lensing selected clusters I: Halo approach and all-sky simulations
• Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation
• Quantifying lost information due to covariance matrix estimation in parameter inference
• Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation
• Fast CMB Power Spectrum Estimation of Temperature and Polarisation with Gabor Transforms
• Response Approach to the Matter Power Spectrum Covariance
• Cosmological N-Body Simulations with a Large-Scale Tidal Field
• Non-Linear Matter Power Spectrum Covariance Matrix Errors and Cosmological Parameter Uncertainties
• A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance
• Fast Generation of Covariance Matrices for Weak Lensing
• Euclid preparation: XII. Optimizing the photometric sample of the Euclid survey for galaxy clustering and galaxy-galaxy lensing analyses
• A Bayesian method for combining theoretical and simulated covariance matrices for large-scale structure surveys
• Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys
• Impact of survey geometry and super-sample covariance on future photometric galaxy surveys
• Exact joint likelihood of pseudo-$C_{\ell }$ estimates from correlated Gaussian cosmological fields
• Lensed CMB power spectrum biases from masking extragalactic sources

Cited by in corpus (7)

• Euclid. I. Overview of the Euclid mission
• KiDS & Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography
• Almanac: Weak Lensing power spectra and map inference on the masked sphere
• Euclid preparation. LII. Forecast impact of super-sample covariance on 3x2pt analysis with Euclid
• The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra
• Almanac: MCMC-based signal extraction of power spectra and maps on the sphere
• Fisher matrix for the angular power spectrum of multi-tracer galaxy surveys