So recently, in chat, I was interested in about what if our universe contains only one CTC (thus making it unlike the Gödel metric, van Stockum dust where there can be more than one CTCs found) and that is the time dimension of the whole universe wrapped back onto itself (meanwhile the spatial dimensions are free to have any topologies so that the resulting spacetime satisfy the einstein field equations. However, I figure I should put this as a question on the main site because it seemed to cover many things.
Suppose this universe is cyclic and include a big bounce (thus both the big bang and big crunch exists), that is, it only differs with what we knew about our universe in that there is only one CTC that is due to the global time direction of the universe looping back to itself. More precisely, any comoving observers will agree that the CTC lies entirely along the time direction.
It is said in the chat that there are nonlocal experiments one can perform to check for CTCs. What are some examples and are they applicable to CTC of this size?
It is also discussed that the CMB in such a universe will contain complex patterns such as the face of he prophet Zarathustra. Are there some examples reference I can read about CMB pattern searches implying about the temporal topology of the universe?
How can we distinguish this type of CTC spacetime with a non CTC spacetime that is also cyclic and also has big bounce as part of its history?
Do such CTC suffer from usual divergence problems of smaller CTCs given how its large size and relativity will allow the fields to not get accumulated easily in a small region due to travelling many times in the CTC?