Keeping It Real: Revisiting a Real-Space Approach to Running Ensembles of Cosmological N-body Simulations

TL;DR

This paper compares real-space and Fourier-space methods for setting initial conditions in cosmological N-body simulations, showing both are similarly accurate when accounting for integral constraint corrections, with implications for modeling large-scale structure.

Contribution

Revisits and refines the real-space initial condition method, demonstrating its accuracy and efficiency relative to Fourier-space approaches when including integral constraint corrections.

Findings

Real-space method performs well in reproducing self-similar behavior.

Correcting for integral constraint bias aligns the accuracy of both methods.

Both methods are similarly effective for large-scale structure simulations.

Abstract

In setting up initial conditions for ensembles of cosmological N-body simulations there are, fundamentally, two choices: either maximizing the correspondence of the initial density field to the assumed fourier-space clustering or, instead, matching to real-space statistics and allowing the DC mode (i.e. overdensity) to vary from box to box as it would in the real universe. As a stringent test of both approaches, I perform ensembles of simulations using power law and a "powerlaw times a bump" model inspired by baryon acoustic oscillations (BAO), exploiting the self-similarity of these initial conditions to quantify the accuracy of the matter-matter two-point correlation results. The real-space method, which was originally proposed by Pen 1997 and implemented by Sirko 2005, performed well in producing the expected self-similar behavior and corroborated the non-linear evolution of the BAO feature observed in conventional simulations, even in the strongly-clustered regime (sigma8 >= 1). In revisiting the real-space method championed by Sirko 2005, it was also noticed that this earlier study overlooked an important integral constraint correction to the correlation function in results from the conventional approach that can be important in LambdaCDM simulations with Lbox =< 1 Gpc/h and on scales r >= Lbox / 10. Rectifying this shows that the fourier space and real space methods are about equally accurate and efficient for modeling the evolution and growth of the correlation function, contrary to previous claims. An appendix provides a useful independent-of-epoch analytic formula for estimating the importance of the integral constraint bias on correlation function measurements in LambdaCDM simulations.