# The Redshift Space Momentum Power Spectrum II: measuring the growth rate from the combined 2MTF and 6dFGSv surveys

## TL;DR

This paper presents a new method to measure the growth rate of cosmic structure using combined galaxy surveys, providing results consistent with standard cosmological models and demonstrating the method's effectiveness.

## Contribution

The authors develop and validate a novel estimator for redshift-space density and momentum power spectra, improving measurements of the growth rate from galaxy velocity data.

## Key findings

- Measured $f\sigma_8$ at $z=0.03$ as 0.404 with uncertainties.
- Validated the method with simulations and corrected for non-Gaussian biases.
- Results align with predictions of General Relativity and the $\Lambda$CDM model.

## Abstract

Measurements of the growth rate of structure, $f\sigma_8$ in the low-redshift Universe allow stringent tests of the cosmological model. In this work, we provide new constraints on $f\sigma_{8}$ at an effective redshift of $z=0.03$ using the combined density and velocity fields measured by the 2MTF and 6dFGSv surveys. We do this by applying a new estimator of the redshift-space density and momentum (density-weighted velocity) power spectra, developed in the first paper of this series, to measured redshifts and peculiar velocities from these datasets. We combine this with models of the density and momentum power spectra in the presence of complex survey geometries and with an ensemble of simulated galaxy catalogues that match the survey selection functions and galaxy bias. We use these simulations to estimate the errors on our measurements and identify possible systematics. In particular, we are able to identify and remove biases caused by the non-Gaussianity of the power spectra by applying the Box-Cox transformation to the power spectra prior to fitting. After thorough validation of our methods we recover a constraint of $f\sigma_8(z_{\mathrm{eff}}=0.03)=0.404^{+0.082}_{-0.081}$ from the combined 2MTF and 6dFGSv data. This measurement is fully consistent with the expectations of General Relativity and the $\Lambda$ Cold Dark Matter cosmological model. It is also comparable and complementary to constraints using different techniques on similar data, affirming the usefulness of our method for extracting cosmology from velocity fields.