  The theoretical basis of dark energy remains unknown and could signify a need
to modify the laws of gravity on cosmological scales. In this study we
investigate how the clustering and motions of galaxies can be used as probes of
modified gravity theories, using galaxy and direct peculiar velocity auto- and
cross-correlation functions. We measure and fit these correlation functions in
simulations of $\Lambda$CDM, DGP, and $f(R)$ cosmologies and, by extracting the
characteristic parameters of each model, we show that these theories can be
distinguished from General Relativity using these measurements. We present
forecasts showing that with sufficiently large data samples, this analysis
technique is a competitive probe that can help place limits on allowed
deviations from GR. For example, a peculiar velocity survey reaching to $z=0.5$
with $20\%$ distance accuracy would constrain model parameters to 3-$\sigma$
confidence limits $\log_{10}|f_{R0}| < -6.45$ for $f(R)$ gravity and $r_c >
2.88 \, c/H_0$ for nDGP, assuming a fiducial GR model.
