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 delta(bc) and decaying relative-velocity perturbation v(bc). 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 delta(bc) and theta(bc) = partial derivative(i)v(bc)(i). We estimate the magnitude of these terms through the excursion set approach. The contribution from v(bc)(2), which has attracted significant attention recently, contributes at subleading (one-loop) order. The relative-density contribution delta(bc) 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 v(bc), leading to a term proportional to mu(2)theta(bc) in the redshift-space galaxy power spectrum P-g(s)(k, mu). Complete expressions of the galaxy power spectrum at one-loop order are given, which contain several new terms.