2004/01/13 by Takahiko Matsubara, Alexander S. Szalay, Adrian Pope +1
Physics and Astronomy · #Astronomy #Astronomy and Astrophysical Research #Astrophysics #Cosmology #Cosmology and Gravitation Theories #Dark energy #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gravitation #Metric expansion of space #Physics #Redshift #Redshift survey #Redshift-space distortions #Universe #astro-ph
paper · pdf · doi:10.1086/382783
published as Astrophys.J. 606 (2004) 1-24 · Submitted to ApJ
arxiv created 2004/01/13 · openalex publication_date 2004/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Eigenmode analysis is one of the most promising methods of analyzing large data sets in ongoing and near-future galaxy surveys. In such analyses, a fast evaluation of the correlation matrix in arbitrary cosmological models is crucial. The observational effects, including peculiar velocity distortions in redshift space, light cone effects, selection effects, and effects of the complex shape of the survey geometry, should be taken into account in the analysis. In the framework of the linear theory of gravitational instability, we provide the methodology to quickly compute the correlation matrix. Our methods are not restricted to shallow redshift surveys: arbitrarily deep samples can be dealt with as well. Therefore, our methods are useful in constraining the geometry of the universe and the dark energy component, as well as the power spectrum of galaxies, since ongoing and near-future galaxy surveys probe the universe at intermediate to deep redshifts, z ~ 0.2-5. In addition to the detailed methods to compute the correlation matrix in three-dimensional redshift surveys, methods to calculate the matrix in two-dimensional projected samples are also provided. Prospects for applying our methods to likelihood estimation of the cosmological parameters are discussed.