Consider a cylindrical universe. Because it is closed (at least in one direction) and non-expanding, I can figure out the distance, say, from the Earth to the same over the full circle of the universe. Now consider I am flying in a relativistic spaceship near the Earth. In this case, if I measure the distance from the ship to the same ship over the full circle in the direction of the flight, this distance would seem to me Lorentz contracted and therefore shorter than the one for the Earth. This way the preferred frame may be chosen as the one with the longest distance over the full circle. This logic is apparently endorsed by some, but does it not violate relativity? For example, if the space is circled only along one dimension, then the curvature is zero and Special Relativity should apply. Should it not?
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$\begingroup$ See also the follow up discussion in Is a preferred reference frame of the universe the old aether? $\endgroup$– John RennieCommented Aug 24, 2017 at 9:45
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If so you wouldn't need a closed universe for your argument, because accoording to that logic it would already be enough to define the prefered reference frame in a way that in this frame the distance between the regular stars and galaxies would be the longest (which happens to be the frame of a comoving observer, who observes no dipole in the cosmic microwave background).
But yes, just like you can chose your frame to be at rest with the cmb in an flat and expanding universe, you also could define your prefered frame by the longest distance to yourself in a nonexpanding closed universe.
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$\begingroup$ My question is if Special Relativity is contradictory in the described cosmology. Per your answer, "you [...] could define your preferred frame by the longest distance to yourself in a non-expanding closed universe". Does this not violates the fundamental postulate of Special Relativity that all inertial frames are equal? $\endgroup$ Commented Aug 24, 2017 at 2:20
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$\begingroup$ They only have equal rights, but they are not the same $\endgroup$– YukterezCommented Aug 24, 2017 at 16:57
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$\begingroup$ Sorry, but I don't see how your equal rights comment is helpful with andwering the question. $\endgroup$ Commented Aug 24, 2017 at 19:38
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$\begingroup$ What I want to say is: yes,you can find a frame of reference where the distance to yourself is the longest in a closed universe, just like you can find a frame of reference where the distance between the galaxies is the longest in a flat one. $\endgroup$– YukterezCommented Aug 24, 2017 at 20:20