  Infrared modifications of General Relativity (GR) can be revealed by
comparing the mass of galaxy clusters estimated from weak lensing to that from
infall kinematics. We measure the 2D galaxy velocity distribution in the
cluster infall region by applying the galaxy infall kinematics (GIK) model
developed by Zu and Weinberg (2013) to two suites of f(R) and Galileon modified
gravity simulations. Despite having distinct screening mechanisms, namely, the
Chameleon and the Vainshtein effects, the f(R) and Galileon clusters exhibit
very similar deviations in their GIK profiles from GR, with ~ 100-200 k/s
enhancement in the characteristic infall velocity at r=5 Mpc/h and 50-100 km/s
broadening in the radial and tangential velocity dispersions across the entire
infall region, for clusters with mass ~ 10^{14} Msol/h at z=0.25. These
deviations are detectable via the GIK reconstruction of the redshift--space
cluster-galaxy cross-correlation function, xi_cg^s(r_p,r_\pi), which shows ~
1-2 Mpc/h increase in the characteristic line-of-sight distance r_\pi^c at
r_p<6 Mpc/h from GR predictions. With overlapping deep imaging and large
redshift surveys in the future, we expect that the GIK modelling of xi_cg^s, in
combination with the stacked weak lensing measurements, will provide powerful
diagnostics of modified gravity theories and the origin of cosmic acceleration.
