REAL-SPACE COSMIC FIELDS FROM REDSHIFT-SPACE DISTRIBUTIONS - GREENS-FUNCTION APPROACH

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 Raiser. We solve this equation by deriving its Green's function; the Green's 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's 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.