I know there is a whole collection of question about the relation between constant X and constant Y in physics. So I should explain why this is not just a gratuitous question on some of the remaining constant combinatorics.
My original motivation was to understand what could be the effect of universe expansion, or of inflation, on the various force fields. This is clearly too general a question, and I had to chose a force that still matters at the scales where expansion makes sense (at least to me). Gravity is the obvious candidate,
The problem is that any question about gravitation runs the risk of getting into specifics I am trying to avoid, such as remarks on the curvature of space (I read carefully answers on other questions about gravitation, questions that had more or less my level of naiveness).
And the best I could com up with, hoping it makes sense, is
Is there a relation between the gravitational constant G and the Hubble constant H ?
i.e. would G be affected, and how, if there was a variation of H for whatever reason ?
And of course: what about a very fast expansion like inflation, possibly considering other forces? But this may already be too much for one question.