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.