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We present the first simultaneous analysis of the galaxy overdensity andpeculiar velocity fields by modelling their cross-covariance. We apply our newmaximum-likelihood approach to data from the 6-degree Field Galaxy Survey(6dFGS), which has the largest single collection of peculiar velocities todate. We present a full derivation of the analytic expression for thecross-covariance between the galaxy overdensity and peculiar velocity fieldsand find direct evidence for a non-zero correlation between the fields onscales up to $\sim50 h^{-1}$ Mpc. When utilising the cross-covariance, ourmeasurement 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 theredshift-space distortion parameter is $\beta=0.341^{+0.062}_{-0.058}$ (18%precision). Both measurements improve by $\sim$20% compared to only using theauto-covariance information. This is consistent with the literature onmultiple-tracer approaches, as well as Fisher matrix forecasts and previousanalyses of 6dFGS. Our measurement of $f\sigma_8$ is consistent with thestandard cosmological model, and we discuss how our approach can be extended totest alternative models of gravity.

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