Optimal Weighting Scheme in Redshift‐Space Power Spectrum Analysis and a Prospect for Measuring the Cosmic Equation of State

We develop a useful formula for power spectrum analysis for high andintermediate redshift galaxy samples, as an extension of the work by Feldman,Kaiser & Peacock (1994). An optimal weight factor, which minimizes the errorsof the power spectrum estimator, is obtained so that the light-cone effect andredshift-space distortions are incorporated. Using this formula, we assess thefeasibility 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 ofthe dark energy. Fisher matrix analysis shows that the LRG sample can besensitive to the equation of state around redshift z=0.13. It is alsodemonstrated that the LRG sample can constrain the equation of state with(1-sigma) error of 10% level, if other fundamental cosmological parameters arewell determined independently. For the useful constraint, we point out theimportance of modeling the bias taking the luminosity dependence into account.We also discuss the optimized strategy to constrain the equation of state usingpower spectrum analysis. For a sample with fixed total number of objects, it ismost advantageous to have the sample with the mean number density $10^{-4}h^3{\rm Mpc}^{-3}$ in the range of the redshift $0.4 \simlt z\simlt 1$.Comment: 27 pages, 7 figures, Final version accepted for publication in Astrophysical Journa