Possible Duality of CBE and Penrose CCC Cyclic Cosmologies

In a cyclic entropy model in which the extroverse is jettisoned at turnaround with a Come Back Empty assumption, we address matching of the contraction scale factor $f(t_T)a(t)$ to the expansion scale factor $a(t)$, where $f(t_T)$ is the ratio at turnaround of the introverse to extroverse radii. Such matching is necessary for infinite cyclicity and fixes the CBE period at $\sim 2.6$ Ty. We then compare such a CBE model with alternative cyclic cosmologies including Penrose Conformal Cyclic Cosmology of period $10^{100}$ y, and speculate that the CBE model may be related to the CCC model by a highly nontrivial isomorphism.