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

Abstract

Measurements of the galaxy power spectrum contain a wealth of information about the Universe. Its optimal extraction is vital if we are to truly understand the micro-physical nature of dark matter and dark energy. In Smith & Marian (2015) we generalized the power spectrum methodology of Feldman et al. (1994) 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 associated with their host halo. In this paradigm we derived the optimal weighting and reconstruction scheme for maximizing the signal-to-noise on a given band power estimate. For a future all-sky flux-limited galaxy redshift survey of depth b_J ~22, we now demonstrate that the optimal weighting scheme does indeed provide improved S/N at the level of ~20% when compared to Feldman et al. (1994) and ~60% relative to Percival et al. (2003), for scales of order k~0.5 Mpc/h. Using a Fisher matrix approach, we show that the cosmological information yield is also increased relative to these alternate methods -- especially the primordial power spectrum amplitude and dark energy equation of state.