TY - JOUR
T1 - Controlling chaos through compactification in cosmological models with a collapsing phase
AU - Wesley, Daniel H.
AU - Steinhardt, Paul J.
AU - Turok, Neil
PY - 2005/9/15
Y1 - 2005/9/15
N2 - We consider the effect of compactification of extra dimensions on the onset of classical chaotic mixmaster behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson- Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close to the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N=1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.
AB - We consider the effect of compactification of extra dimensions on the onset of classical chaotic mixmaster behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson- Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close to the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N=1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.
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U2 - 10.1103/PhysRevD.72.063513
DO - 10.1103/PhysRevD.72.063513
M3 - Article
AN - SCOPUS:29744442065
SN - 1550-7998
VL - 72
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 6
M1 - 063513
ER -