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

TL;DR

This paper develops an optimal weighting scheme for measuring the galaxy power spectrum that improves signal-to-noise ratio and enhances cosmological parameter estimation in large galaxy surveys.

Contribution

It extends previous methods by incorporating galaxy formation physics to optimize power spectrum measurements for future surveys.

Findings

Optimal weighting improves S/N by ~20% over previous methods.

Enhanced cosmological parameter constraints, especially on primordial power spectrum and dark energy.

Demonstrates practical benefits for upcoming large-scale galaxy surveys.

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.