Constraining the Cosmological Constant from Large-Scale Redshift-Space Clustering

We show how the cosmological constant can be estimated from redshift surveys at different redshifts, using maximum likelihood techniques. The apparent redshift-space clustering on large scales (≳20 h -1 Mpc) is affected in the radial direction by infall, and curvature influences the apparent correlations in the transverse direction. The relative strengths of the two effects will strongly vary with redshift. Using a simple idealized survey geometry, we compute the smoothed correlation matrix of the redshift-space correlation function and the Fisher matrix for Ω M and Ω Λ . These represent the best possible measurement of these parameters given the geometry. We find that the likelihood contours are turning, according to the behavior of the angular diameter distance relation. The clustering measures from redshift surveys at intermediate to high redshifts can provide a surprisingly tight constraint on Ω Λ . We also estimate confidence contours for real survey geometries, using the Sloan Digital Sky Survey Luminous Red Galaxy and QSO surveys as specific examples. We believe that this method will become a practical tool to constrain the nature of dark energy.