Fast Generation of Covariance Matrices for Weak Lensing

Abstract

Upcoming weak lensing surveys will probe large fractions of the sky with unprecedented accuracy. To infer cosmological constraints, a large ensemble of survey simulations are required to accurately model cosmological observables and their covariances. We develop a parallelized multi-lens-plane pipeline called UFalcon, designed to generate full-sky weak lensing maps from lightcones within a minimal runtime. It makes use of L-PICOLA, an approximate numerical code, which provides a fast and accurate alternative to cosmological $N$-Body simulations. The UFalcon maps are constructed by nesting 2 simulations covering a redshift-range from $z=0.1$ to $1.5$ without replicating the simulation volume. We compute the convergence and projected overdensity maps for L-PICOLA in the lightcone or snapshot mode. The generation of such a map, including the L-PICOLA simulation, takes about 3 hours walltime on 220 cores. We use the maps to calculate the spherical harmonic power spectra, which we compare to theoretical predictions and to UFalcon results generated using the full $N$-Body code GADGET-2. We then compute the covariance matrix of the full-sky spherical harmonic power spectra using 150 UFalcon maps based on L-PICOLA in lightcone mode. We consider the PDF, the higher-order moments and the variance of the smoothed field variance to quantify the accuracy of the covariance matrix, which we find to be a few percent for scales $\ell \sim 10^2$ to $10^3$. We test the impact of this level of accuracy on cosmological constraints using an optimistic survey configuration, and find that the final results are robust to this level of uncertainty. The speed and accuracy of our developed pipeline provides a basis to also include further important features such as masking, varying noise and will allow us to compute covariance matrices for models beyond $\Lambda$CDM. [abridged]

20 pages, 7 figures

References in corpus (13)

• Introducing the Illustris Project: Simulating the coevolution of dark and visible matter in the Universe
• Properties of galaxies reproduced by a hydrodynamic simulation
• Introducing the Illustris Project: the evolution of galaxy populations across cosmic time
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• The Illustris simulation: the evolving population of black holes across cosmic time
• Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments
• The onion universe: all sky lightcone simulations in spherical shells
• Full-Sky Weak Lensing Simulation with 70 Billion Particles
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Matter Power Spectrum Covariance Matrix from the DEUS-PUR ΛCDM simulations: Mass Resolution and non-Gaussian Errors
• Modelling the Transfer Function for the Dark Energy Survey
• Quantifying lost information due to covariance matrix estimation in parameter inference
• ICE-COLA: fast simulations for weak lensing observables

Cited by in corpus (18)

• DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
• Large-scale dark matter simulations
• Cosmological constraints with deep learning from KiDS-450 weak lensing maps
• Fast cosmic web simulations with generative adversarial networks
• Cosmological Forecast for non-Gaussian Statistics in large-scale weak Lensing Surveys
• A Full $w$CDM Analysis of KiDS-1000 Weak Lensing Maps using Deep Learning
• Effects of baryons on weak lensing peak statistics
• CosmoGridV1: a simulated $w$CDM theory prediction for map-level cosmological inference
• Redshift requirements for cosmic shear with intrinsic alignment
• Towards a full $w$CDM map-based analysis for weak lensing surveys
• Euclid: Covariance of weak lensing pseudo-$C_{\ell }$ estimates. Calculation, comparison to simulations, and dependence on survey geometry
• Box Replication Effects in Weak Lensing Light-cone Construction
• A tomographic spherical mass map emulator of the KiDS-1000 survey using conditional generative adversarial networks
• Assessing theoretical uncertainties for cosmological constraints from weak lensing surveys
• A Hamiltonian, post-Born, three-dimensional, on-the-fly ray tracing algorithm for gravitational lensing
• Dark Energy Survey Year 3 results: Cosmology with peaks using an emulator approach
• Interpretability of deep-learning methods applied to large-scale structure surveys
• $\text{SBi3PCF:}$ Simulation-based inference with the integrated 3PCF