TL;DR
This paper investigates the nature of an infinite past in cyclic universe models, addressing geodesic completeness and probability of universe cycling, concluding that the total number of universes has been infinite for an arbitrarily long time.
Contribution
It provides positive answers to key questions about the infinite past in cyclic cosmology, challenging previous no-go theorems and analyzing universe probabilities.
Findings
Infinite null geodesic into the past is possible in cyclic models
There is an adequate probability for universe cycling after infinite time
The total number of universes has been infinite for an arbitrarily long duration
Abstract
We address two questions about the past for infinitely cyclic cosmology. The first is whether it can contain an infinite length null geodesic into the past in view of the Borde-Guth-Vilenkin (BGV) "no-go" theorem, The second is whether, given that a small fraction of spawned universes fail to cycle, there is an adequate probability for a successful universe after an infinite time. We give positive answers to both questions then show that in infinite cyclicity the total number of universes has been infinite for an arbitrarily long time.
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