Have you looked at Penrose's stuff on the cyclical universe and how the universe could expand to a point where it "forgets" its scale, thus the very large universe is mathematically the same as a singularity which prompts the next big bang. Rinse and repeat.
https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology
https://en.wikipedia.org/wiki/Conformal_cyclic_cosmology