The Effect of Modified Gravity on the Odds of the Bound Violations of the Turn-Around Radii

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.