Maybe when gravity gets very weak, as it does on cosmic scales, quantum effects come into play and cause it to deviate from the usual inverse-square law
The final measurement in this group of related experiments was a test of the inverse-square law
of gravitation on the scale of meters to kilometers.
0 mm--large enough to be detectable but small enough not to be ruled out by tests of the inverse-square law
Astronomer Stacy McGaugh (University of Maryland) puts it this way: "Suppose Newton, upon studying the solar system, would have formulated an inverse-cube law, claiming that the observed inverse-square law
is the result of some mysterious, undetected dark matter.
Acknowledging that Newton had succeeded in solving the mathematical problem but incensed that his own name is not mentioned in a section of Newton's treatise recently read at a Royal Society meeting, Hooke has demanded that Newton give him proper credit in the Principia for the inverse-square law
Test of the Gravitational Inverse-Square Law
at Laboratory Distances.
Thus, the inverse-square law
of gravitation is derived by methods of hydrodynamics based on a sink flow model of particles.
Meanwhile, tabletop experiments are testing Newton's inverse-square law
at submillimeter scales to see if gravity leaks into extra dimensions.
But at scales corresponding to the sizes of these extra dimensions, gravity could become as strong as the other forces--so strong that it violates Newton's inverse-square law