Submanifolds in space-time with unphysical extra dimensions, cosmology and warped brane world models

TL;DR

This paper demonstrates how four-dimensional cosmological models and five-dimensional warped brane world models can be represented as submanifolds within flat higher-dimensional Minkowski space through explicit coordinate transformations.

Contribution

It provides explicit coordinate transformations linking 4D cosmologies and 5D warped brane models to flat Minkowski space, illustrating their geometric equivalence.

Findings

Explicit transformations for 4D cosmologies in 5D Minkowski space.

Analogous transformations for warped brane world models.

Multiple examples illustrating the submanifold embeddings.

Abstract

The explicit coordinate transformations which show the equivalence between a four-dimensional spatially flat cosmology and an appropriate submanifold in the flat five-dimensional Minkowski space-time are presented. Analogous procedure is made for the case of five-dimensional warped brane world models. Several examples are presented.