On 4-dimensional cosmological models locally embedded in a 5-dimensional Ricci-flat space

TL;DR

This paper constructs 4D cosmological models from 5D Ricci-flat solutions using Campbell's theorem and induced-matter theory, highlighting how extra-dimensional wave solutions can influence observable cosmology.

Contribution

It demonstrates a method to derive 4D cosmological models from 5D Ricci-flat spaces via Campbell's theorem and induced-matter theory, emphasizing wave propagation along the extra dimension.

Findings

Models derived from 5D Ricci-flat space exhibit wave-like features.

Dimensional reduction in the Jordan frame produces realistic cosmological scenarios.

The approach links higher-dimensional wave solutions to 4D cosmology.

Abstract

We employ a theorem due to Campbell to build some simple 4-dimensional cosmological models which originate from solutions describing waves propagating along the extra-dimension of a 5-dimensional Ricci-flat space. The dimensional reduction is performed in the Jordan frame according to the induced-matter theory of Wesson.