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
