Accelerating Universe and Dynamical Compactification of Extra Dimensions

Abstract

We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter as the space-time part of the higher dimensional energy-momentum tensor, a 4-dimensional decaying cosmological term is appeared as $\Lambda \sim R^{-2}$, playing the role of an evolving dark energy in the universe. The resulting field equations yield the exponential solutions for the scale factors. These exponential behaviors may account for the dynamical compactification of extra dimensions and the accelerating expansion of the 4-dimensional universe in terms of the Hubble parameter. The acceleration of universe may be explained by the negative pressure of the exotic matter. It is shown that the rate of compactification of higher dimensions depends on the dimension, $D$. We then obtain the Wheeler-DeWitt equation and find the general exact solutions in $D$-dimensions. A good correspondence between the classical solutions and the Wheeler-DeWitt solutions, in any dimension $D$, is obtained.

16 pages, 18 figures, minor adjustments, further remarks, references added

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• Parameters of cosmological models and recent astronomical observations
• Cosmological Implications of 5-dimensional Brans-Dicke Theory
• 4+1 dimensional homogeneous anisotropic string cosmological models
• Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime
• Higher Dimensional Cosmology: Relations among the radii of two homogeneous spaces
• Multidimensional gravitational model with anisotropic pressure
• $\Lambda$CDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe
• Dynamical System Analysis of a Five-Dimensional Cosmological Model
• Anisotropic evolution of D-dimensional FRW spacetime