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Supersonic Relative Velocity between Dark Matter and Baryons: A Review

In this review we summarize the effect of relative supersonic velocities between gas and dark matter created right after recombination on astrophysics and cosmology. The relative velocities formally introduce a second order effect on the standard results and thus have been neglected in the framework of linear theory. However, when properly considered, the velocities yield a non-perturbative contribution to the growth of structures which is then inherited by the majority of cosmic signals coming from redshifts above z ~ 10, and in certain cases may even propagate to various low-redshift observables such as the Baryon Acoustic Oscillations measured from the distribution of galaxies. At higher redshifts, the supersonic velocities have thus strong impact affecting the abundance of first star forming halos in an inhomogeneous way, hindering creation of the first stars, leaving traces in the redshifted 21-cm signal of neutral hydrogen, as well as having other important contributions at high redshifts all of which we review in this manuscript.