The Cosmic Code Comparison Project

TL;DR

The paper addresses the challenge of achieving high-precision predictions for nonlinear cosmic structure by conducting a comprehensive cross-code comparison of 10 gravity-only cosmological codes spanning grid, tree, and hybrid methods. It employs identical initial conditions and a ParaView-based analysis framework to quantify differences in halos, mass functions, density environments, and the matter power spectrum across codes. Findings show robust agreement (better than ~5%) for the halo mass function and outer halo profiles, while differences emerge in the inner halo regions and especially in the power spectrum at higher $k$ and in AMR/TPM implementations due to resolution and algorithmic nuances. The work demonstrates ParaView’s utility for benchmarking and highlights areas where larger simulation boxes and refined force resolution are needed to meet the precision demands of upcoming cosmological surveys.

Abstract

Current and upcoming cosmological observations allow us to probe structures on smaller and smaller scales, entering highly nonlinear regimes. In order to obtain theoretical predictions in these regimes, large cosmological simulations have to be carried out. The promised high accuracy from observations make the simulation task very demanding: the simulations have to be at least as accurate as the observations. This requirement can only be fulfilled by carrying out an extensive code validation program. The first step of such a program is the comparison of different cosmology codes including gravitation interactions only. In this paper we extend a recently carried out code comparison project to include five more simulation codes. We restrict our analysis to a small cosmological volume which allows us to investigate properties of halos. For the matter power spectrum and the mass function, the previous results hold, with the codes agreeing at the 10% level over wide dynamic ranges. We extend our analysis to the comparison of halo profiles and investigate the halo count as a function of local density. We introduce and discuss ParaView as a flexible analysis tool for cosmological simulations, the use of which immensely simplifies the code comparison task.

Figures (14)

• Figure 1: Screenshot of the comparative visualization manager in ParaView. Upper row: results from four different codes, zoomed into a dense region of the simulations. Particles are displayed as arrow glyphs, colored with respect to their velocity magnitude. Lower row: same region, the particles now displayed simply as dots.
• Figure 2: A subset of the 20,000 particles at $z=0$ from the GADGET-2 simulation (left) and the Enzo simulation (right). The particles are shown with vector arrow glyphs which are sized and colored by their velocity magnitude (blue: slowest, red: fastest).
• Figure 3: Halo profiles for the five heaviest halos in the simulation. The black line shows the best-fit NFW profile to the TPM simulation, mainly to guide the eye. In the outer regions all codes agree very well. In the inner regions the fall-off of the grid codes is as expected due to resolution limitations. The fall-off point can be predicted from the finite force resolution and agrees well with the results. The middle panel in each plot shows the ratio of the different codes with respect to GADGET-2. The lower panels show only the four grid codes and the ratio with respect to MC$^2$.
• Figure 4: Projected and normalized two-dimensional density for Halo 1 from PMM (left) and TreePM (right). TreePM has a slightly higher density in the inner region of the halo than PMM, as to be expected from the different force resolutions. Overall the agreement is very good.
• Figure 5: Two-dimensional contour plot of the projected density for Halo 3 from MC$^2$, FLASH, GADGET-2, and HOT (left upper to right lower plot). White: particles, black: contour smoothed with a Gaussian Filter.