  It is speculated how dark energy in a brane world can help reconcile an
infinitely cyclic cosmology with the second law of thermodynamics. A cyclic
cosmology is described, in which dark energy leads to a turnaround at a time,
extremely shortly before the would-be Big Rip, at which both volume and entropy
of our universe decrease by a gigantic factor, while very many independent
similarly small contracting universes are spawned. The entropy of our universe
decreases almost to zero at turnaround but increases for the remainder of the
cycle by a vanishingly small amount during contraction, empty of matter, then
by a large factor during inflationary expansion.
