Accelerating Universe and Dynamical Compactification of Extra Dimensions

TL;DR

This paper explores a higher-dimensional cosmological model with exotic matter, showing how it can explain the universe's accelerated expansion and compactification of extra dimensions through exponential solutions and quantum wave functions.

Contribution

It introduces a novel higher-dimensional cosmology with exotic matter that results in an evolving dark energy and provides exact solutions to the Wheeler-DeWitt equation across dimensions.

Findings

Exponential solutions for scale factors explain acceleration and compactification.

The decaying cosmological term acts as evolving dark energy.

Classical and quantum solutions show good correspondence across 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.