When we look in all directions, we see distant objects red-shifted, with the size of the red-shift correlated with the distance from us.
As I understand it, the consensus among cosmologists is that this observation is best explained by the expansion of space across intergalactic distances, a.k.a "Hubble flow", described by the FLRW metric. This makes sense to me.
However, it seems that this could also be explained by the Earth being some kind of special spot in the universe, and for some other reason everything around us is physically moving away from us, and the farther things are moving away faster, without any expansion of space; with simply static space-time. To be clear, this anthropocentric theory does not seem compelling to me, and I am not advocating for it.
My question is this:
Is there any physical evidence that can distinguish between "Hubble flow" and some kind of bizarre anthropocentric universe where everything just happens to have been propelled away from the Earth in a very specific way?
I can see that the expanding space theory is simpler and more elegant, but I'm looking for some kind of observable evidence (that has been observed, or could be observed in the future) that could falsify one or the other theory.