A local measurement of the growth rate from peculiar velocities and galaxy clustering correlations in the 6dF Galaxy Survey

Galaxy peculiar velocities provide an integral source of cosmological information that can be harnessed to measure the growth rate of large scale structure and constrain possible extensions to General Relativity. In this work, we present a method for extracting the information contained within galaxy peculiar velocities through an ensemble of direct peculiar velocity and galaxy clustering correlation statistics, including the effects of redshift space distortions, using data from the 6-degree Field Galaxy Survey. Our method compares the auto- and cross-correlation function multipoles of these observables, with respect to the local line of sight, with the predictions of cosmological models. We find that the uncertainty in our measurement is improved when combining these two sources of information in comparison to fitting to either peculiar velocity or clustering information separately. When combining velocity and density statistics in the range $27 < s < 123 \, h^{-1}$ Mpc we obtain a value for the local growth rate of $f\sigma_8 = 0.358 \pm 0.075$ and for the linear redshift distortion parameter $\beta = 0.298 \pm 0.065$, recovering both with $20.9$ per cent and $21.8$ per cent accuracy respectively. We conclude this work by comparing our measurement with other recent local measurements of the growth rate, spanning different datasets and methodologies. We find that our results are in broad agreement with those in the literature and are fully consistent with $\Lambda$CDM cosmology. Our methods can be readily scaled to analyse upcoming large galaxy surveys and achieve accurate tests of the cosmological model.