1999/08/31 by Takahiko Matsubara
Mathematics · Physics and Astronomy · #Astrophysics #Classical mechanics #Correlation #Correlation function (quantum field theory) #Cosmology and Gravitation Theories #Curvature #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Geometry #Mathematics #Observer (physics) #Physics #Quantum mechanics #Redshift #Redshift survey #Redshift-space distortions #Space (punctuation) #Statistical physics #Stellar, planetary, and galactic studies #Theoretical physics #Universe #astro-ph
paper · pdf · doi:10.1086/308827
45 pages including 9 figures, To Appear in Astrophys. J. 535 (2000)
arxiv created 2000/02/08 · openalex publication_date 2000/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A general formula for the correlation function in redshift space is derived in linear theory. The formula simultaneously includes wide-angle effects and cosmological distortions. The formula is applicable to any pair with arbitrary angle θ between lines of sight, and arbitrary redshifts z 1 , z 2 , which are not necessarily small. The effects of the spatial curvature both on geometry and on the fluctuation spectrum are properly taken into account, and thus our formula holds in a Friedman-Lemaître universe with arbitrary cosmological parameters Ω 0 and λ 0 . We illustrate the pattern of the resulting correlation function with several models, and also show that the validity region of the conventional distant observer approximation is θ ≤ 10°.