Submanifolds in spacetime with an auxiliary unphysical extra dimension and four-dimensional open and closed FRW universes

TL;DR

This paper demonstrates how four-dimensional open and closed FRW universes can be represented as submanifolds within a five-dimensional pseudo-Euclidean space-time, providing explicit coordinate transformations for this equivalence.

Contribution

It provides explicit coordinate transformations showing the equivalence between 4D FRW universes and submanifolds in 5D space-time, highlighting the role of an auxiliary unphysical extra dimension.

Findings

Explicit transformations between FRW metrics and 5D submanifolds

Unified geometric representation of open and closed universes

Insight into higher-dimensional embeddings of cosmological models

Abstract

The explicit coordinate transformations which show the equivalence between the FRW metrics of four-dimensional open and closed universes and the metrics induced on appropriate submanifolds in a five-dimensional pseudo-Euclidean space-time are presented.