2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214229In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE-condition ({\it Comes Back Empty}) imposes a lower bound on the number $N_{\rm cp}$ of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state $w = p/ρ= -1 - ϕ$ with $ϕ> 0$. More accurate measurement of $ϕ$ will constrain $N_{\rm cp}$. The critical density $ρ_c$ in the model has a lower bound $ρ_c \ge (10^9 {\rm GeV})^4$ or $ρ_c \ge (10^{18} {\rm GeV})^4$ when the smallest bound state has size $10^{-15}$m, or $10^{-35}$m, respectively.23 pages, 3 figures, typos fixedHigh Energy Physics - TheoryAstrophysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Phenomenologytext