Effect of relative velocity and density perturbations between baryons and dark matter on the clustering of galaxies

Prerecombination acoustic oscillations induce nonadiabatic perturbations between baryons and dark matter, corresponding to a constant relative-density ₁₂ and decaying relative-velocity perturbation v₁₂. Due to their significant large-scale correlations and prominent baryon acoustic oscillation (BAO) features, these modes are potentially important for the use of the BAO as standard ruler. We present a complete treatment of the effects of the baryon--cold dark matter perturbations on galaxy clustering in the context of a rigorous perturbative bias expansion. The leading effects are proportional to ₁₂ and ₁₂=₈v₁₂^i. We estimate the magnitude of these terms through the excursion set approach. The contribution from v₁₂^2, which has attracted significant attention recently, contributes at subleading (one-loop) order. The relative-density contribution ₁₂ is expected to be by far the largest contribution. We also point out contributions to the galaxy velocity bias, the largest of which is simply v₁₂, leading to a term ^2₁₂ in the redshift-space galaxy power spectrum P₆^s (k, ). Complete expressions of the galaxy power spectrum at one-loop order are given, which contain several new terms.