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Pre-recombination acoustic oscillations induce non-adiabatic perturbationsbetween baryons and dark matter, corresponding to a constant relative-density$\delta_{bc}$ and decaying relative-velocity perturbation $\vec{v}_{bc}$. Dueto their significant large-scale correlations and prominent baryon acousticoscillation (BAO) features, these modes are potentially important for the useof the BAO as standard ruler. We present a complete treatment of the effects ofthe baryon-CDM perturbations on galaxy clustering in the context of a rigorousperturbative bias expansion. The leading effects are proportional to$\delta_{bc}$ and $\theta_{bc} = \partial_i v_{bc}^i$. We estimate themagnitude of these terms through the excursion set approach. The contributionfrom $v_{bc}^2$, which has attracted significant attention recently,contributes at subleading (1-loop) order. The relative-density contribution$\delta_{bc}$ is expected to be by far the largest contribution. We also pointout contributions to the galaxy velocity bias, the largest of which is simply$v_{bc}$, leading to a term $\propto \mu^2\theta_{bc}$ in the redshift-spacegalaxy power spectrum $P_g^s(k,\mu)$. Complete expressions of the galaxy powerspectrum at 1-loop order are given, which contain several new terms.

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