Cosmological Perturbation Theory as a Tool for Estimating Box-Scale
  Effects in N-body Simulations
  In performing cosmological N-body simulations, it is widely appreciated that
the growth of structure on the largest scales within a simulation box will be
inhibited by the finite size of the simulation volume. Following ideas set
forth in Seto (1999), this paper shows that standard (a.k.a. 1-loop)
cosmological perturbation theory (SPT) can be used to predict, in an
approximate way, the deleterious effect of the box scale on the power spectrum
of density fluctuations in simulation volumes. Alternatively, this approach can
be used to quickly estimate post facto the effect of the box scale on power
spectrum results from existing simulations. In this way SPT can help determine
whether larger box sizes or other more-sophisticated methods are needed to
achieve a particular level of precision for a given application (e.g.
simulations to measure the non-linear evolution of baryon acoustic
oscillations). I focus on SPT in this note and show that its predictions differ
only by about a factor of two or less from the measured suppression inferred
from both powerlaw and $\Lambda$CDM $N$-body simulations. It should be possible
to improve the accuracy of these predictions through using more-sophisticated
perturbation theory models. An appendix compares power spectrum measurements
from the powerlaw simulations at outputs where box-scale effects are minimal to
perturbation theory models and previously-published fitting functions. These
power spectrum measurements are included with this paper to aid efforts to
develop new perturbation theory models.
