On fast Generation of Cosmological Random Fields

Abstract

The statistical translation invariance of cosmological random fields is broken by a finite survey boundary, correlating the observable Fourier modes. Standard methods for generating Gaussian fields either neglect these correlations, or are costly, or both. Here we report on a fast and exact simulation method applicable to a wide class of two-point statistics that requires the simulation of a periodic grid of only twice the survey side with fast Fourier transforms. Super-survey modes, dominating the covariance of power spectra beyond linear scales in galaxy surveys and causing the correlation of large and small scales, "beat coupling", or "super-sample" covariance, are precisely accounted for in non-linear transformations of the Gaussian field. As an application, we simulate the CFHTLS $\sim 7^{\circ }\times 7^{\circ }$ W1 galaxy density field, modeled as a Poisson sampling of a lognormal density field. We show that our simulations produce power spectra, $A^{\ast }$-power spectra, counts-in-cells probability distributions as well as covariances perfectly consistent with the data. In addition, our technique reproduces the information plateau beyond linear scales as observed previously in Sloan Digital Sky Survey galaxy catalogs and in $N$-body simulations. Our method is thus an efficient yet powerful simulation and prediction tool for galaxy survey data and covariances.

arXiv comment8 pages, 5 figures, matches version accepted for publication in MNRAS

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• The impact of super-survey modes on cosmological constraints from cosmic shear fields
• An empirical nonlinear power spectrum overdensity-response