Optimal Weighting Scheme in Redshift-space Power Spectrum Analysis and a Prospect for Measuring the Cosmic Equation of State
Abstract
We develop a useful formula for power spectrum analysis for high and intermediate redshift galaxy samples, as an extension to the work by Feldman, Kaiser & Peacock (1994). An optimal weight factor, which minimizes the errors of the power spectrum estimator, is obtained so that the light-cone effect and redshift-space distortions are incorporated. Using this formula, we assess the feasibility of the power spectrum analysis with the luminous red galaxy (LRG) sample in the Sloan Digital Sky Survey as a probe of the equation of state of the dark energy. Fisher matrix analysis shows that the LRG sample can be sensitive to the equation of state around redshift z = 0.13. It is also demonstrated that the LRG sample can constrain the equation of state with 1 sigma error of 10 ~ 15%, if other fundamental cosmological parameters are well determined independently. We also discuss the optimized strategy to constrain the equation of state using power spectrum analysis. For a sample with fixed total number of objects, it is most advantageous to have the sample with the mean number density 10^{-4} h^3{Mpc}^3 in the range of the redshift 0.4 <~ z <~ 1.Keywords
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