High-precision predictions for the acoustic scale in the non-linear
  regime
  We measure shifts of the acoustic scale due to nonlinear growth and redshift
distortions to a high precision using a very large volume of
high-force-resolution simulations. We compare results from various sets of
simulations that differ in their force, volume, and mass resolution. We find a
consistency within 1.5-sigma for shift values from different simulations and
derive shift alpha(z) -1 = (0.300\pm 0.015)% [D(z)/D(0)]^{2} using our fiducial
set. We find a strong correlation with a non-unity slope between shifts in real
space and in redshift space and a weak correlation between the initial redshift
and low redshift. Density-field reconstruction not only removes the mean shifts
and reduces errors on the mean, but also tightens the correlations: after
reconstruction, we recover a slope of near unity for the correlation between
the real and redshift space and restore a strong correlation between the low
and the initial redshifts. We derive propagators and mode-coupling terms from
our N-body simulations and compared with Zeldovich approximation and the shifts
measured from the chi^2 fitting, respectively. We interpret the propagator and
the mode-coupling term of a nonlinear density field in the context of an
average and a dispersion of its complex Fourier coefficients relative to those
of the linear density field; from these two terms, we derive a signal-to-noise
ratio of the acoustic peak measurement. We attempt to improve our
reconstruction method by implementing 2LPT and iterative operations: we obtain
little improvement. The Fisher matrix estimates of uncertainty in the acoustic
scale is tested using 5000 (Gpc/h)^3 of cosmological PM simulations from
Takahashi et al. (2009). (abridged)
