What is the optimal way to measure the galaxy power spectrum?

Abstract

Measurements of the galaxy power spectrum contain a wealth of cosmological information. In Smith &Marian, we generalized the power spectrum methodology of Feldman et al. to take into account the key tenets of galaxy formation: galaxies form and reside exclusively in dark matter haloes; a given dark matter halo may host galaxies of various luminosities; galaxies inherit the large-scale bias of their host halo. In this paradigm,we derived the optimal weighting scheme for maximizing the signal-to-noise (S/N) on a given band power estimate. For a future all-sky flux-limited galaxy redshift survey of depth bJ > 22, we demonstrate that the optimal weighting scheme does indeed provide improved S/N at the level of ~20 per cent when compared to Feldman et al. and ~60 per cent relative to Percival et al., for scales of the order of k ~ 0.5 h Mpc-1. Using a Fisher matrix approach, we show the cosmological information yield is also increased relative to these alternate methods - especially the primordial power spectrum amplitude and dark energy equation of state. Caveats: uncertainties in cluster masses, non-linear halo bias and redshift distortions may reduce information gains.