Cosmological $N$-body simulations with suppressed variance

TL;DR

This paper introduces a variance reduction technique for cosmological N-body simulations using fixed and paired initial conditions, significantly improving precision and reducing computational costs.

Contribution

The authors propose a novel fixed-and-paired simulation method that minimizes variance, allowing accurate predictions with fewer simulations compared to traditional approaches.

Findings

Predictions from fixed-pair simulations match ensemble averages on non-linear scales.

The method reduces the number of simulations needed for precise clustering statistics.

Analytic argument shows non-Gaussian corrections do not bias mean property predictions.

Abstract

We present and test a method that dramatically reduces variance arising from the sparse sampling of wavemodes in cosmological simulations. The method uses two simulations which are fixed (the initial Fourier mode amplitudes are fixed to the ensemble average power spectrum) and paired (with initial modes exactly out of phase). We measure the power spectrum, monopole and quadrupole redshift-space correlation functions, halo mass function and reduced bispectrum at $z=1$. By these measures, predictions from a fixed pair can be as precise on non-linear scales as an average over 50 traditional simulations. The fixing procedure introduces a non-Gaussian correction to the initial conditions; we give an analytic argument showing why the simulations are still able to predict the mean properties of the Gaussian ensemble. We anticipate that the method will drive down the computational time requirements for accurate large-scale explorations of galaxy bias and clustering statistics, enabling more precise comparisons with theoretical models, and facilitating the use of numerical simulations in cosmological data interpretation.