The Dynamical Evolution of 3-Space in a Higher Dimensional Steady State Universe

TL;DR

This paper explores the evolution of a higher-dimensional universe with a cosmological constant, revealing new dynamics such as oscillating expansion rates and analyzing how such a universe appears to four-dimensional observers.

Contribution

It introduces new cosmological solutions in higher dimensions with specific volume and energy constraints, expanding understanding of universe dynamics with extra dimensions.

Findings

Time-varying deceleration parameter including oscillations

External space dynamics influenced by higher-dimensional constraints

Implications for four-dimensional perception of higher-dimensional universe

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.