I am referring to yet another version as the classical twin paradox.

In my version the moving apart of the twins is entirely induced by space expansion between them and they move apart each other at a very high speed, conceivably even higher than the local speed of light.

After some time space itself contracts again so that they meet again.

The question is: Is there an age difference between the two?

Is it correct to say that both stayed in the same inertial frame so that there is not even a paradox and no resulting age difference or is the situation more subtle?


Your question is hypothetical since the universe is almost certainly not closed and will not recollapse (pace Andrei Linde). However if we assume an FLRW metric and a closed universe then all comoving observers will agree on the time between the Big Bang and the Big Crunch so the twins will have aged the same amount.

If you have in mind a different scenario you'll have to be clearer what you want. For example the Hubble expansion of space will not separate the twins if they start at the same spacetime point (unless that point is the Big Bang). Also note that if you intend some artifical expansion caused by moving masses around then the twins will almost certainly have aged different amounts even when they are moving freely. This is because in GR multiple geodesics between two spacetime points can have different elapsed proper times.


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