A Generally Covariant Model of Spacetime as a 4-Brane in 4+1 Flat Dimensions

TL;DR

This paper presents a simple, fully covariant toy model of a closed FLRW spacetime as a 4-brane embedded in five-dimensional flat space, deriving the metric dynamically from scalar fields without curvature terms.

Contribution

It introduces a novel covariant model of spacetime as a 4-brane in 4+1 dimensions using scalar fields and a string-like potential, with the metric determined dynamically.

Findings

Successfully constructs a covariant FLRW cosmology from scalar fields.

Demonstrates the metric is uniquely determined by the dynamical equations.

Shows that an SO(4) invariant ansatz suffices for the model.

Abstract

We construct a simple toy model of a closed FLRW spacetime by starting from a flat five dimensional scalar field space. The action contains no curvature terms. A string-like potential is used for the field space. The model is fully covariant and the spacetime metric is uniquely determined from the dynamical equations of the metric tensor. An SO(4) invariant ansatz for the scalar fields is shown to be sufficient to build the FLRW cosmology.