Towards breaking the Omega-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 Omega-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 Omega-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 nonlinear but local bias; accounting for stochasticity of bias is left for further study.