Suppose you have a metal rod, of vast length, floating in space. From it's center-of-mass reference frame it is assumed to be at rest with respect to the CMB.
The rod will have some degree of internal forces (eg tension) holding it in shape. Suppose then that the rod is so long that if one were to observe one end of the rod from the other, they would find the remote region of space getting further away from them.
What forces would the rod experience due to expansion, if any?
Would it experience a 'pull' from either end?
If there were dust particles stationary relative to the CMB near each end of the rod, would they see the rod shrink in length / would the rod observe the dust particles moving away from the center of mass?
If the rod is a conductor (thermal or electric) I'm not entirely sure what to expect to see.
(I suspect this may have been answered on this site somewhere already, if so I could not find a similar enough wording of this problem)