The redshiftspace momentum power spectrum  I. Optimal estimation from peculiar velocity surveys
Abstract
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 redshiftspace momentum power spectrum from such surveys. We provide a comprehensive theoretical and practical framework for estimating and fitting this from data, analogous to wellunderstood 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 (PV) measurement errors. We finish with a proofofconcept using realistic mock galaxy catalogues, which demonstrates that we can measure and fit both the redshiftspace galaxy density and momentum power spectra from PV surveys and that including the latter substantially improves our constraints on the growth rate of structure. We also provide theoretical descriptions for modelling the nonlinear redshiftspace density and momentum power spectrum multipoles, and forecasting the constraints on cosmological parameters using the Fisher information contained in these measurements for arbitrary weights. These may be useful for measurements of the galaxy density power spectrum even in the absence of peculiar velocities.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2019
 DOI:
 10.1093/mnras/stz1403
 arXiv:
 arXiv:1906.02875
 Bibcode:
 2019MNRAS.487.5209H
 Keywords:

 cosmological parameters;
 cosmology: observations;
 largescale structure of the Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 22+3 Pages, 14 Figures. Accepted for publication in MNRAS. This is the first in "The RedshiftSpace Momentum Power Spectrum" series of papers