Cyclic Period in the CBE Model
  In a cyclic entropy model in which the extroverse is jettisoned at turnaround with a Come Back Empty (CBE) assumption, we address matching of the contaction scale factor $\hat{a}(t)=f(t_T){a}(t)$ 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 $\sim 2.6Ty$. 
Paul H Frampton
gr-qc astro-ph.CO