  The detailed nature of dark energy remains a mystery, leaving the possibility
that its effects might be explained by changes to the laws of gravity on large
scales. The peculiar velocities of galaxies directly trace the strength of
gravity on cosmic scales and provide a means to further constrain such models.
We generate constraints on different scenarios of gravitational physics by
measuring peculiar velocity and galaxy clustering two-point correlations, using
redshifts and distances from the 6-degree Field Galaxy Survey and the Sloan
Digital Sky Survey Peculiar Velocity samples, and fitting them against models
characteristic of different cosmologies. Our best-fitting results are all found
to be in statistical agreement with General Relativity, in which context we
measure the low-redshift growth of structure to be $f\sigma_8 =
0.329^{+0.081}_{-0.083}$, consistent with the prediction of the standard
$\Lambda$CDM model. We also fit the modified gravity scenarios of
Dvali-Gabadadze-Porrati (nDGP) and a Hu-Sawicki model of $f(R)$ gravity,
finding the $2\sigma$ limit of their characteristic parameters to be
$r_cH_0/c>6.987$ and $-\log_{10}(|f_{R0}|)>4.703$, respectively. These
constraints are comparable to other literature values, though it should be
noted that they are significantly affected by the prior adopted for their
characteristic parameters. When applied to much larger upcoming peculiar
velocity surveys such as DESI, this method will place rapidly-improving
constraints on modified gravity models of cosmic expansion and growth.
