Improving Initial Conditions for Cosmological $N$-Body Simulations

In cosmological $N$-body simulations, the representation of dark matter as discrete "macroparticles" suppresses the growth of structure, such that simulations no longer reproduce linear theory on small scales near $k_{\rm Nyquist}$. Marcos et al. demonstrate that this is due to sparse sampling of modes near $k_{\rm Nyquist}$ and that the often-assumed continuum growing modes are not proper growing modes of the particle system. We develop initial conditions that respect the particle linear theory growing modes and then rescale the mode amplitudes to account for growth suppression. These ICs also allow us to take advantage of our very accurate $N$-body code Abacus to implement 2LPT in configuration space. The combination of 2LPT and rescaling improves the accuracy of the late-time power spectra, halo mass functions, and halo clustering. In particular, we achieve 1% accuracy in the power spectrum down to $k_{\rm Nyquist}$, versus $k_{\rm Nyquist}/4$ without rescaling or $k_{\rm Nyquist}/13$ without 2LPT, relative to an oversampled reference simulation. We anticipate that our 2LPT will be useful for large simulations where FFTs are expensive and that rescaling will be useful for suites of medium-resolution simulations used in cosmic emulators and galaxy survey mock catalogs. Code to generate initial conditions is available at https://github.com/lgarrison/zeldovich-PLT