On fast Generation of Cosmological Random Fields

Understand

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.