Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Mert Ergen, Metin Arık

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.

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

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.

Paper Structure

This paper contains 9 sections, 39 equations.

Table of Contents

  1. Introduction
  2. Cartesian Coordinates for FLRW Metric with $k = 1$
  3. Proposed Lagrangian Density
  4. Scale Invariant Assumption For The Action
  5. Constant magnitude $\phi$-field $\chi$-field Assumption
  6. Conclusion
  7. Author Contribution
  8. Data Availability
  9. Funding Declaration