I meant that apart from the proton and the electron there is nothing else around that affects them in any meaningful way. So there will be expansion. And force, in its usual sense, really does not exist, but as we know the expansion of the universe happens with acceleration and so we can...
TL;DR Summary: Express through the Hubble constant the force that acts on the hydrogen atom due to the expansion of the universe
We have a hydrogen atom, in a gravitationally bound system nothing interesting happens to it. Let's put it in an empty world with only an electron and a proton...