  The turn-around radii of the galaxy groups show the imprint of a long battle
between their self-gravitational forces and the accelerating space. The
standard $\Lambda$CDM cosmology based on the general relativity (GR) predicts
the existence of an upper bound on the expectation value of the turn-around
radius which is rarely violated by individual galaxy groups. We speculate that
a deviation of the gravitational law from GR on the cosmological scale could
cause an appreciable shift of the mean turn-around radius to higher values and
make the occurrence of the bound violation more probable. Analyzing the data
from high-resolution N-body simulations for two specific models with modified
gravity (MG) and the standard GR+$\Lambda$CDM cosmology, we determine the
turn-around radii of the massive Rockstar groups from the peculiar motions of
the galactic halos located in the bound zone where the fifth force generated by
MG is expected to be at most partially shielded. We detect a $4\sigma$ signal
of difference in the odds of the bound violations between a fiducial MG and the
GR models, proving that the odds of the bound violations increase with the
strength of the fifth force produced by the presence of MG. The advantage of
using the odds of the bound violations as a complementary diagnostics to probe
the nature of gravity is discussed.
