2DFFTLog: efficient computation of realspace covariance matrices for galaxy clustering and weak lensing
Abstract
Accurate covariance matrices for twopoint functions are critical for inferring cosmological parameters in likelihood analyses of largescale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2DFFTLog algorithm for efficient, accurate, and numerically stable computation of nonGaussian realspace covariances for both 3D and projected statistics. The 2DFFTLog algorithm is easily extended to perform realspace binaveraging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3like and a Rubin Observatory's Legacy Survey of Space and Time Year 1like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular binaveraged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code COSMOCOV for computing the realspace covariances with or without the flatsky approximation is released along with this paper.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2020
 DOI:
 10.1093/mnras/staa1726
 arXiv:
 arXiv:2004.04833
 Bibcode:
 2020MNRAS.497.2699F
 Keywords:

 cosmological parameters;
 dark energy;
 largescale structure of Universe;
 cosmology: theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 MNRAS accepted