Perturbation Theory Reloaded Ii: Non-linear Bias, Baryon Acoustic Oscillations and Millennium Simulation in Real Space

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 ≤ z ≤ 6. 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, DA(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. Subject headings: cosmology : theory — large-scale structure of universe