Complementary Cosmological Simulations

TL;DR

This paper introduces a novel method using phase-shifted paired simulations to measure and mitigate cosmic variance effects in cosmological N-body simulations, improving accuracy in statistical analyses.

Contribution

It presents a new approach with paired simulations that reduces cosmic variance bias, validated on the Millennium simulation, enhancing the reliability of cosmological statistics.

Findings

Average power spectrum matches nonlinear spectra at late times.

Complementary pairs can estimate cosmic variance effects.

Resolved baryon acoustic oscillation features in simulations.

Abstract

Cosmic variance limits the accuracy of cosmological N-body simulations, introducing bias in statistics such as the power spectrum, halo mass function, or the cosmic shear. We provide new methods to measure and reduce the effect of cosmic variance in existing and new simulations. We ran pairs of simulations using phase-shifted initial conditions with matching amplitudes. We set the initial amplitudes of the Fourier modes to ensure that the average power spectrum of the pair is equal to the cosmic mean power spectrum from linear theory. The average power spectrum of a pair of such simulations remains consistent with the estimated nonlinear spectra of the state-of-the-art methods even at late times. We also show that the effect of cosmic variance on any analysis involving a cosmological simulation can be estimated using the complementary pair of the original simulation. To demonstrate the effectiveness of our novel technique, we simulated a complementary pair of the original Millennium run and quantified the degree to which cosmic variance affected its the power spectrum. The average power spectrum of the original and complementary Millennium simulation was able to directly resolve the baryon acoustic oscillation features.