Modern cosmologies from empty Kaluza-Klein solutions in 5D

TL;DR

This paper demonstrates that certain five-dimensional vacuum solutions can generate diverse four-dimensional cosmological models, bridging older Kaluza-Klein theories with modern noncompactified 5D gravity frameworks like induced-matter and braneworld models.

Contribution

It systematically investigates the embedding of 5D vacuum solutions into 4D cosmologies, offering a new perspective complementary to existing 5D relativity approaches.

Findings

Generated a variety of 4D cosmological models from 5D solutions.

Connected old Kaluza-Klein solutions with modern 5D gravity theories.

Provided a systematic methodology for embedding 5D solutions into 4D cosmology.

Abstract

We show that the empty five-dimensional solutions of Davidson-Sonnenschtein-Vozmediano, {\em Phys. Rev.} {\bf D32} (1985)1330, in the "old" Kaluza-Klein gravity, under appropriate interpretation can generate an ample variety of cosmological models in 4D, which include the higher-dimensional modifications to general relativity predicted by "modern" versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld theories. This is the first time that these solutions are investigated in a systematic way as embeddings for cosmological models in 4D. They provide a different formulation, which is complementary to the approaches used in current versions of 5D relativity.