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Paper IPM / P / 7273  


Abstract:  
We study a (4 + D)dimensional KaluzaKlein cosmology with a RobertsonWalker type metric having two scale factors a and R, corresponding to a Ddimensional internal space and fourdimensional universe, respectively. By introducing exotic matter as the spacetime part of the higher dimensional energymomentum tensor, a fourdimensional decaying cosmological term appears as R2, 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 behaviours may account for the dynamical compactification of extra dimensions and the accelerating expansion of the fourdimensional universe in terms of the Hubble parameter. The acceleration of the 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 WheelerDeWitt equation and find the general exact solutions in D dimensions. A good correspondence between the classical solutions and the WheelerDeWitt solutions in any dimension, D, is obtained.
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