Does the inverse square law hold indefinitely for gravity?

[Jake Banner]

If the inverse square law for gravity varies with distance or distribution of matter, might the need for “dark matter” be obviated?

 

[PeterDonis]

If the inverse square law for gravity varies with distance or distribution of matter

Then you would need to develop a theory that predicted this, while also correctly predicting all the other experimental data we have on gravity. Bear in mind that, in General Relativity, the inverse square law is not a fundamental postulate; it is a derived result for a particular solution of the Einstein Field Equation (the one that describes the spacetime geometry around a static, spherically symmetric object), and an approximate one at that (since in GR gravity is not treated as a force and so "inverse square law" only makes sense to begin with in an appropriate approximation--in this case the weak field, slow motion limit). So from the standpoint of GR, you can't just change the inverse square law and leave everything else the same; you would have to change the Einstein Field Equation, which would change all of the predictions of GR (and nobody has figured out how to do that in a way that does not make the changed predictions inconsistent with experiment).

There have been other theories proposed (such as MOND) that modify the inverse square law, but none of them can match the predictive power of GR throughout all the regimes that have been tested; they can make correct predictions for particular things (such as galaxy rotation curves), but that's all.

 

[Vanadium 50]

There have been other theories proposed (such as MOND)

To be clear, MOND does not take a force law that depends only on position and turn it into a different force law that depends only on position. It turns it into a force law that depends the same way on position but also on local acceleration. It is known that there is no way to explain dark matter by any force law that depends only on position.