  We calculate the non-linear galaxy power spectrum in real space, including
non-linear distortion of the Baryon Acoustic Oscillations, using the standard
3rd-order perturbation theory (PT). The calculation is based upon the
assumption that the number density of galaxies is a local function of the
underlying, non-linear density field. The galaxy bias is allowed to be both
non-linear and stochastic. We show that the PT calculation agrees with the
galaxy power spectrum estimated from the Millennium Simulation, in the weakly
non-linear regime (defined by the matter power spectrum) at high redshifts,
$1\le z\le6$. We also show that, once 3 free parameters characterizing galaxy
bias are marginalized over, the PT power spectrum fit to the Millennium
Simulation data yields unbiased estimates of the distance scale, $D$, to within
the statistical error. This distance scale corresponds to the angular diameter
distance, $D_A(z)$, and the expansion rate, $H(z)$, in real galaxy surveys. Our
results presented in this paper are still restricted to real space. The future
work should include the effects of non-linear redshift space distortion.
Nevertheless, our results indicate that non-linear galaxy bias in the weakly
non-linear regime at high redshifts is reasonably under control.
