Real-space cosmic fields from redshift-space distributions: a Green function approach

Abstract

We present a new method for reconstructing the cosmological density, peculiar velocity and peculiar gravitational potential on large scales from redshift data. We remove the distorting effects of line-of-sight peculiar motions by using the linear theory of gravitational instability, in which the potential is the solution to a linear partial differential equation first derived by Kaiser. We solve this equation by deriving its Green function; the Green functions for the peculiar velocity and the real-space density follow directly. Reconstruction of the cosmic fields is thus reduced to integration over redshift space with the appropriate Green function kernel. Our algorithm has a single input parameter, beta=Omega^0.6/b, where b is the linear bias factor and Omega is the cosmological density parameter. We discuss the virtues of this method for error control, for estimating beta, and for constraining the bias mechanism.