Towards breaking the Ω-bias degeneracy in density–velocity comparisons

I derive a second-order local relation between the redshift-space mass density field and the real-space velocity field. This relation can be useful for comparisons between the cosmic density and peculiar velocity fields, for a number of reasons. First, relating the real-space velocity directly to the redshift-space density enables one to avoid the Ω-dependent reconstruction of the density field in real space. Secondly, the reconstruction of the three-dimensional velocity field in redshift space, questionable because of its vorticity, is also unnecessary. Finally, a similar relation between the galaxy density field and the velocity field offers a way to break the Ω-bias degeneracy in density–velocity comparisons, when combined with an additional measurement of the redshift-space galaxy skewness. I derive the latter relation under the assumption of non-linear but local bias; accounting for stochasticity of bias is left for further study.