On fast Generation of Cosmological Random Fields

TL;DR

This paper introduces a fast, exact simulation method for cosmological random fields that accurately accounts for survey boundary effects and super-survey modes, improving the modeling of galaxy survey data.

Contribution

The authors develop a computationally efficient simulation technique that precisely incorporates super-survey modes and boundary effects for cosmological fields, applicable to a wide range of two-point statistics.

Findings

Simulations match observed power spectra and covariances.

Method reproduces the information plateau beyond linear scales.

Efficiently models survey boundary effects and super-sample covariance.

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, $A^*$-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.