Cyclic Universe
[361] "Turnaround in Cyclic Cosmology" by L. Baum and P.H. Frampton.
Phys. Rev. Lett. 96, 071301 (2007). hep-th/0610213.
It was argued in [361] that dark energy in a brane world can reconcile an infinitely
cyclic cosmology with the second law of thermodynamics. Using phantom dark energy,
the universe turns around a trillion trillionth of a second (or less) before the would-be
Big Rip. At this time, the universe fragments into a large number of causal patches,
only one of which is retained. The entropy thereby drops to zero. The contracting
universe contains only dark energy, together with a small number of low energy photons.
Other causal patches each spawn a separate contracting universe.
[365]"Entropy of Contracting Universe in Cyclic Cosmology"
by L. Baum and P.H. Frampton.
hep-th/0703162.
In [365], the content of the contracting
universe was examined and the entropy shown
to be
accurately zero because only a negligible number
of spawned universes contain
a photon.
An anthropic argument was presented of why
the dark energy equation of state
w should not be too close to w=-1.
[367]"Cyclic Universe and Infinite Past" by P.H. Frampton. arXiv:0705.2730.
The issue of time goes to minus infinity was discussed in [367].
It was shown that there can
exist an infinite length
null geodesic. The number of universes is infinite
and has been equal
to a constant infinite number, Aleph-zero,
for an arbitrarily
long time into the past.
[379]"Constraints on Deflation from the Equation of State of Dark Energy"
by L. Baum, P.H. Frampton and S. Matsuzaki. arXiv:0801.4420 [hep-th]
The "comes back empty" (CBE) condition, meaning that the contracting universe
contains no matter including no black holes, relates the dark energy equation
of state to the number of causal patches at turnaround. In [379], the values
of critical energy density were also constrained by the smallest bound system
disintegrated at deflation, be it a nucleon or a "presently point particle" (PPP)
now regarded as pointlike, like a quark or lepton, but assumed to be a bound state
if studied at the Planck length of 10**-35 meters.
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