There are many questions about space expansion, its cause, or its effects. But I have the feeling we never get straight and simple answers. I do not expect answers to be simple in general, but I wondered whether I could use simple reasonning to answer some questions. Disclaimer: I do not know General Relativity.
One answer I have seen many times is that space expansion is not strong enough to disrupt most structures of the universe, such as an atom or a solar system, because there are stronger forces binding these structures. This argument led me to think that space expansion acts as a force, but there was no hint as to the nature of that force or its strength.
So, I tried to evaluate it on my own, which I do below, and my question is whether my simplistic reasonning is valid, and whether my terminology is correct (and to cut short criticism, that led me to understand that it shows only indirectly as a force).
Since an independent body is simply carried away by the Hubble flow, I first need to consider a simple system that will naturally oppose it. Short of a non existing anchor to block an object against the Hubble flow, I thought of a set up that is similar to Arthur C. Clarke's space elevator, which balances the elevator below a geosynchronous satellite with a counterweight above the satellite (on the outerspace side).
Basically I am considering two objects $A$ and $B$ with the same mass $m$. The two objects are connected with a very long and strong massless rope of length $2l$, and I call $O$ the middle of the rope (I recommend ropes made by General Products).
Since this system is symetrical, I suppose that both masses $A$ and $B$ are pulled away from $O$ by space expansion, but are stopped by the rope, the pull on one object being balanced by an opposite pull on the other. Since everything is happening on the line $(A,B)$, we can analyze the system in one dimension, using scalars rather than vectors.
The relative speed due to expansion applied to 2 independent objects at distance $x$ is defined by $v=H_0x$. Deriving this, we have the acceleration of their relative expansion induced motion $\gamma=H_0v=H_0^2x$.
Object $A$ would thus move away from $O$ with an acceleration $\gamma_A=H_0^2l$, but is prevented by the rope where $B$ is balancing it. Hence $A$ is accelerated in the opposite sense with respect to the Hubble flow by the pull of the rope. Hence the pull on the rope is $F_A=mH_0^2x$. It is opposed in $O$ by a pull from B that is equal and opposite.
This shows several things:
the force produced by space expansion is proportional to the mass of the object it is applied to. It is not really a force but an acceleration;
this force (or acceleration) appears when the object cannot follow normally the expanding Hubble flow because it is bound to a structure larger than itself;
this force is centrifugal with respect to the structure, and must be balanced by an opposite centripetal force originating from the larger structure;
this force is proportional to the size of the structure (probably something like the distance to its center of mass),
and the proportionality constant is the square of the Hubble constant $H_0$, which, given the already very small value of $H_0$, is extremely small.
Assuming it is correct, that is the kind of answer I would have liked to some questions, but did not see.
I could not very well give that myself as an answer because no question was asked exactly that way, and it would be very presomptuous anyway, considering that I know nearly nothing of general relativity.
So I am simply asking: is it correct, and is the terminology adequate?
If I am not correct, is there a better treatment of this question that can be understood at about the same level?
Or is it fully correct and should I reorganize my question as a question plus an answer by myself?
