  At the time of recombination, baryons and photons decoupled and the sound
speed in the baryonic fluid dropped from relativistic to the thermal velocities
of the hydrogen atoms. This is less than the relative velocities of baryons and
dark matter computed via linear perturbation theory, so we infer that there are
supersonic coherent flows of the baryons relative to the underlying potential
wells created by the dark matter. As a result, the advection of small-scale
perturbations (near the baryonic Jeans scale) by large-scale velocity flows is
important for the formation of the first baryonic structures. This effect
involves a quadratic term in the cosmological perturbation theory equations and
hence has not been included in studies based on linear perturbation theory. We
show that the relative motion suppresses the abundance of the first bound
objects, even if one only investigates dark matter haloes, and leads to
qualitative changes in their spatial distribution, such as introducing
scale-dependent bias and stochasticity. We discuss the possible observable
implications for high-redshift galaxy clustering and reionization.
