# Improving constraints on the growth rate of structure by modelling the density-velocity cross-correlation in the 6dF Galaxy Survey

## TL;DR

This paper introduces a new method to analyze galaxy and velocity data jointly, improving constraints on the universe's structure growth rate by modeling their cross-correlation, with application to the 6dFGS dataset.

## Contribution

The paper develops a maximum-likelihood approach to model the cross-covariance of galaxy density and velocity fields, providing the first direct evidence of their correlation and improved growth rate measurements.

## Key findings

- Detected non-zero density-velocity correlation up to 50 h^{-1} Mpc.
- Measured fσ8(z=0) = 0.424 with 15% precision.
- Achieved 20% improvement in growth rate constraints over previous methods.

## Abstract

We present the first simultaneous analysis of the galaxy overdensity and peculiar velocity fields by modelling their cross-covariance. We apply our new maximum-likelihood approach to data from the 6-degree Field Galaxy Survey (6dFGS), which has the largest single collection of peculiar velocities to date. We present a full derivation of the analytic expression for the cross-covariance between the galaxy overdensity and peculiar velocity fields and find direct evidence for a non-zero correlation between the fields on scales up to $\sim50 h^{-1}$ Mpc. When utilising the cross-covariance, our measurement of the normalised growth rate of structure is $f\sigma_8(z=0) = 0.424^{+0.067}_{-0.064}$ (15% precision), and our measurement of the redshift-space distortion parameter is $\beta=0.341^{+0.062}_{-0.058}$ (18% precision). Both measurements improve by $\sim$20% compared to only using the auto-covariance information. This is consistent with the literature on multiple-tracer approaches, as well as Fisher matrix forecasts and previous analyses of 6dFGS. Our measurement of $f\sigma_8$ is consistent with the standard cosmological model, and we discuss how our approach can be extended to test alternative models of gravity.