A constant correlation between external and internal expansion rates yields exact Bianchi type-I solutions whose effective dark energy mimics a cosmological constant at late times and a steady-state universe for negative correlation.
The Dynamical Evolution of 3-Space in a Higher Dimensional Steady State Universe
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abstract
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject to two constraints that (i) the total volume scale factor of the universe is constant and (ii) the effective energy density is constant. We obtain various interesting new dynamics for the external space that yield a time varying deceleration parameter including oscillating cases when the flat/curved external and curved/flat internal spaces are considered. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the extra dimensions.
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Role of internal space correlations in the dynamics of a higher-dimensional Bianchi type-I universe: shear scalar and Hubble parameter perspectives
A constant correlation between external and internal expansion rates yields exact Bianchi type-I solutions whose effective dark energy mimics a cosmological constant at late times and a steady-state universe for negative correlation.