Cosmological Implications of a Non-Separable 5D Solution of the Vacuum Einstein Field Equations

TL;DR

This paper derives exact 5D vacuum solutions with non-separable metric functions, revealing diverse cosmological behaviors including models without a big bang and evolving matter equations of state, impacting higher-dimensional cosmology theories.

Contribution

It presents a new class of exact 5D vacuum solutions with non-separable metrics, expanding the understanding of higher-dimensional cosmological models.

Findings

Some models lack a big bang singularity.

The equation of state evolves from radiation-like to Milne-like.

Null geodesics projections align with standard 4D cosmology.

Abstract

An exact class of solutions of the 5D vacuum Einstein field equations (EFEs) is obtained. The metric coefficients are found to be non-separable functions of time and the extra coordinate $l$ and the induced metric on $l$ = constant hypersurfaces has the form of a Friedmann-Robertson-Walker cosmology. The 5D manifold and 3D and 4D submanifolds are in general curved, which distinguishes this solution from previous ones in the literature. The singularity structure of the manifold is explored: some models in the class do not exhibit a big bang, while other exhibit a big bang and a big crunch. For the models with an initial singularity, the equation of state of the induced matter evolves from radiation like at early epochs to Milne-like at late times and the big bang manifests itself as a singular hypersurface in 5D. The projection of comoving 5D null geodesics onto the 4D submanifold is shown to be compatible with standard 4D comoving trajectories, while the expansion of 5D null congruences is shown to be in line with conventional notions of the Hubble expansion.