What I grasp is roughly the following, we know, that you could construct a scalar field, part of a spacetime that solves relativity, that would show almost no e

What I grasp is roughly the following, we know, that you could construct a scalar field, part of a spacetime that solves relativity, that would show almost no effect on a weak gravity environment (it's mostly undetectable, unless close to a massive object). But in massive environments, we could in principle detect the effects of a non-trivial field (i.e. make predictions, and try to observe them). Essentially, build a theory (perturb the theory), and make a testable prediction that works on the large scale, but would be hard or impossible to observe on a weak gravity environment (for some definition of weak, I think they mean something less massive than a star). They ask whether or not you can do something like this with a more complex, vector field (i.e. a new force/particle). It's all very theoretical. But it may give an avenue to find new physics, maybe even explain dark matter/energy.