The Redshift-Space Momentum Power Spectrum I: Optimal Estimation From Peculiar Velocity Surveys

Understand

Low redshift surveys of galaxy peculiar velocities provide a wealth of cosmological information.

• We revisit the idea of extracting this information by directly measuring the redshift-space momentum power spectrum from such surveys.
• We provide a comprehensive theoretical and practical framework for estimating and fitting this from data, analogous to well understood techniques used to measure the galaxy density power spectrum from redshift surveys.
• We formally derive a new estimator, which includes the effects of shot noise and survey geometry; we evaluate the variance of the estimator in the Gaussian regime; we compute the optimal weights for the estimator; we demonstrate that the measurements are Gaussian distributed, allowing for easy extraction of cosmological parameters; and we explore the effects of peculiar velocity measurement errors.