A Determination of Dark Matter Bispectrum with a Large Set of N -body Simulations

We use a set of numerical N -body simulations to study the large-scale behavior of the reduced bispectrum of dark matter and compare the results with the second-order perturbation theory and the halo models for different halo mass functions. We find that the second-order perturbation theory (PT2) agrees with the simulations fairly well on large scales of k < 0.05 hMpc, but it shows a signature of deviation as the scale goes down. Even on the largest scale where the bispectrum can be measured reasonably well in our simulations, the inconsistency between PT2 and the simulations appears for the colinear triangle shapes. For the halo model, we find that it can only serve as a qualitative method to help study the behavior of Q on large scales and also on relatively small scales. The failure of second-order perturbation theory will also affect the precise determination of the halo models, since they are connected through the 3-halo term in the halo model. The 2-halo term has too much contribution on the large scales, which is the main reason for the halo model to overpredict the bispectrum on the large scales. Since neither of the models can provide a satisfying description for the bispectrum on scales k ∼ 0.1 hMpc for the requirement of precision cosmology, we release the reduced bispectrum of dark matter on a large range of scales for future analytical modeling of the bispectrum. Subject headings: gravitational lensing—dark matter— cosmology: theory— galaxies: formation