Keeping It Real: Revisiting a Real-Space Approach to Running Ensembles
  of Cosmological N-body Simulations
  In setting up initial conditions for ensembles of cosmological N-body
simulations there are, fundamentally, two choices: either maximizing the
correspondence of the initial density field to the assumed fourier-space
clustering or, instead, matching to real-space statistics and allowing the DC
mode (i.e. overdensity) to vary from box to box as it would in the real
universe. As a stringent test of both approaches, I perform ensembles of
simulations using power law and a "powerlaw times a bump" model inspired by
baryon acoustic oscillations (BAO), exploiting the self-similarity of these
initial conditions to quantify the accuracy of the matter-matter two-point
correlation results. The real-space method, which was originally proposed by
Pen 1997 and implemented by Sirko 2005, performed well in producing the
expected self-similar behavior and corroborated the non-linear evolution of the
BAO feature observed in conventional simulations, even in the
strongly-clustered regime (sigma8 >= 1). In revisiting the real-space method
championed by Sirko 2005, it was also noticed that this earlier study
overlooked an important integral constraint correction to the correlation
function in results from the conventional approach that can be important in
LambdaCDM simulations with Lbox =< 1 Gpc/h and on scales r >= Lbox / 10.
Rectifying this shows that the fourier space and real space methods are about
equally accurate and efficient for modeling the evolution and growth of the
correlation function, contrary to previous claims. An appendix provides a
useful independent-of-epoch analytic formula for estimating the importance of
the integral constraint bias on correlation function measurements in LambdaCDM
simulations.
