Fast generation of ensembles of cosmological N-body simulations via
  mode-resampling
  We present an algorithm for quickly generating multiple realizations of
N-body simulations to be used, for example, for cosmological parameter
estimation from surveys of large-scale structure. Our algorithm uses a new
method to resample the large-scale (Gaussian-distributed) Fourier modes in a
periodic N-body simulation box in a manner that properly accounts for the
nonlinear mode-coupling between large and small scales. We find that our method
for adding new large-scale mode realizations recovers the nonlinear power
spectrum to sub-percent accuracy on scales larger than about half the Nyquist
frequency of the simulation box. Using 20 N-body simulations, we obtain a power
spectrum covariance matrix estimate that matches the estimator in Takahashi et
al. (2009) (from 5000 simulations) with < 20% errors in all matrix elements.
Comparing the rates of convergence, we determine that our algorithm requires ~
8 times fewer simulations to achieve a given error tolerance in estimates of
the power spectrum covariance matrix. The degree of success of our algorithm
indicates that we understand the main physical processes that give rise to the
correlations in the matter power spectrum. Namely, the large-scale Fourier
modes modulate both the degree of structure growth through the variation in the
effective local matter density and also the spatial frequency of small-scale
perturbations through large-scale displacements. We expect our algorithm to be
useful for noise modeling when constraining cosmological parameters from weak
lensing (cosmic shear) and galaxy surveys, rescaling summary statistics of
N-body simulations for new cosmological parameter values, and any applications
where the influence of Fourier modes larger than the simulation size must be
accounted for.
