Possible Duality of CBE and Penrose CCC Cyclic Cosmologies

TL;DR

This paper explores a cyclic entropy cosmology with a Come Back Empty assumption, matching contraction and expansion phases, and compares it to Penrose's Conformal Cyclic Cosmology, suggesting a possible deep connection.

Contribution

It introduces a method for matching contraction and expansion scale factors in a cyclic entropy model and proposes a potential isomorphism with Penrose's CCC.

Findings

CBE period estimated at approximately 2.6 trillion years

Matching conditions for cyclicity are established

Possible theoretical link between CBE and CCC models suggested

Abstract

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.