2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118640Dark energy in a brane world reconciles an infinitely cyclic cosmology with the second law of thermodynamics. At turnaround one causal patch with no matter and vanishing entropy is retained for the contraction.7 pages latex. Talk presented at Workshop on Origin of Mass and Strong Coupling Gauge Theories. Nagoya, Japan. 21-24 November,2006Astrophysicstext