Reconstruction Analysis of Galaxy Redshift Surveys: A Hybrid Reconstruction Method

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Abstract
In reconstruction analysis of a galaxy redshift survey, one works backward from the observed galaxy distribution to the primordial density field in the same region of space, then evolves the primordial fluctuations forward in time with an N-body code. A reconstruction incorporates assumptions about the values of cosmological parameters, the properties of primordial fluctuations, and the "biasing" relation between galaxies and mass. These assumptions can be tested by comparing the reconstructed galaxy distribution to the observed distribution, and to peculiar velocity data when available. This paper presents a hybrid reconstruction method that combines the "Gaussianization" technique of Weinberg with the dynamical schemes of Nusser & Dekel and Gramann. We test the method on N-body simulations and on N-body mock catalogs designed to mimic the depth and geometry of the Point Source Catalog Redshift Survey and the Optical Redshift Survey. The hybrid method is more accurate than Gaussianization or dynamical reconstruction alone. Matching the observed morphology of clustering can set limits on the bias factor b independently of Ω. Matching cluster velocity dispersions and the redshift-space distortions of the correlation function ξ(s, μ) constrains the parameter combination β ≈ Ω0.6/b. Relative to linear or quasi-linear approximations, a fully nonlinear reconstruction makes more accurate predictions of ξ(s, μ) for a given β, reducing the systematic biases of β measurements and offering further possibilities for breaking the degeneracy between Ω and b. Reconstruction also circumvents the cosmic variance noise that limits conventional analyses of ξ(s, μ), since the orientations of large, coherent structures in the observed galaxy distribution are reproduced in the reconstruction. Finally, reconstruction can improve the determination of Ω and b from joint analyses of redshift and peculiar velocity surveys because it provides a fully nonlinear prediction of the peculiar velocity distribution at each point in redshift space.
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