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

21 pages, 12 figures, 1 table; the version accepted for publication in General Relativity and Gravitation

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Cited by in corpus (7)

• Relaxing cosmological tensions with a sign switching cosmological constant
• Screening $\Lambda$ in a new modified gravity model
• Late Time Acceleration of the 3-Space in a Higher Dimensional Steady State Universe in Dilaton Gravity
• Accelerated Expansion of the Universe in a Higher Dimensional Modified Gravity with Euler-Poincaré Terms
• $\Lambda$CDM cosmology with a quiescent anisotropy in a higher dimensional steady state universe
• Role of internal space correlations in the dynamics of a higher-dimensional Bianchi type-I universe: shear scalar and Hubble parameter perspectives
• General solution of a cosmological model induced from higher dimensions using a kinematical constraint