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 of 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% level, if other fundamental cosmological parameters are well determined independently. For the useful constraint, we point out the importance of modeling the bias taking the luminosity dependence into account. 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 $10^{-4} h^3{\rm Mpc}^{-3}$ in the range of the redshift $0.4 \simlt z\simlt 1$.