Ozgur Akarsu, Tekin Dereli
A class of cosmological solutions of higher dimensional Einstein field
equations with the energy-momentum tensor of a homogeneous, isotropic fluid as
the source are considered with an anisotropic metric that includes the direct
sum of a 3-dimensional (physical, flat) external space metric and an
n-dimensional (compact, flat) internal space metric. A simple kinematical
constraint is postulated that correlates the expansion rates of the external
and internal spaces in terms of a real parameter \lambda. A specific solution
for which both the external and internal spaces expand at different rates is
given analytically for n=3. Assuming that the internal dimensions were at
Planck length scales at the beginning t=0, the external space starts with a Big
Bang and the external and internal spaces both reach the same size after
10^{-176} Gyr. Then during the lifetime of the observed universe (13.7 Gyr),
the external dimensions would expand 10^{59} times while the internal
dimensions expand only 1.49 times. The effective four dimensional universe
would exhibit a behavior consistent with our current understanding of the
observed universe. It would start in a stiff fluid dominated phase and evolve
through radiation dominated and pressureless matter dominated phases,
eventually going into a de Sitter phase at late times.
View original:
http://arxiv.org/abs/1201.4545
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