Day 399

Saturday.

2006MNRAS.371.1188H  (arXiv:astro-ph/0511416)
On measuring the covariance matrix of the non-linear power spectrum from simulations
Hamilton, Rimes, Scoccimarro

Estimate the covariance of PS of a statistically homogeneous and isotropic density field from a single periodic simulation by applying a set of weightings to the density field, and by measuring the scatter in PS between different weightings.  Recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power.  Numerical tests reveal that at non-linear scales the variance of power estimated by the weighting method substantially exceeds that estimated from a simple ensemble method.  Argue that this discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by NL gravitational growth to the beat mode between them.  Beat-coupling appears whenever NL power is measured from Fourier modes with a finite spread of wavevector, and is therefore preset in the weightings method but not in the ensemble method.  Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width.  Surprisingly, the beat-coupling contribution dominates the covariance of power at NL scales, so that, counter-intuitively, it is expected that the covariance of NL power in galaxy surveys is dominated not by small-scale structure, but rather by beat-coupling to the largest scales of the survey.