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

## TL;DR

This paper develops a comprehensive framework for extracting the redshift-space momentum power spectrum from galaxy peculiar velocity surveys, improving cosmological parameter constraints by including momentum information.

## Contribution

It introduces a new estimator for the redshift-space momentum power spectrum, accounting for shot noise, survey geometry, and measurement errors, with a proof-of-concept demonstration.

## Key findings

- Successfully measured and fitted galaxy density and momentum power spectra from mock surveys.
- Including momentum power spectrum improves constraints on the growth rate of structure.
- Provided theoretical models for non-linear redshift-space power spectrum multipoles.

## 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 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. We finish with a proof-of-concept using realistic mock galaxy catalogues, which demonstrates that we can measure and fit both the redshift-space galaxy density and momentum power spectra from peculiar velocity surveys and that including the latter substantially improves our constraints on the growth rate of structure. We also provide theoretical descriptions for modelling the non-linear redshift-space 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.