Classical evolution of subspaces

We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.

Note:

29 pages, 9 figures

derivative: high
energy: high
boundary condition
gravitation
mathematical methods

References(47)

Figures(9)

The Hierarchy problem and new dimensions at a millimeter

Nima Arkani-Hamed
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•
DOI:
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Grand unification at intermediate mass scales through extra dimensions

Keith R. Dienes
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Tony Gherghetta
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- hep-ph/9806292
•
DOI:
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Neutrino masses from large extra dimensions

Nima Arkani-Hamed
(
- SLAC
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,
Savas Dimopoulos
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G.R. Dvali
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Large extra dimensions and cosmological problems

Glenn D. Starkman
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U. Gunther
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Brian R. Greene
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Sean M. Carroll
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Sergei V. Ketov
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Hiroshi Nakada
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