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, $1le zle6$. 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.
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