4-D homogeneous isotropic cosmological models generated by the 5-D vacuum

TL;DR

This paper explores how 4D cosmological models derived from 5D vacuum solutions can simulate matter and determine the equation of state based on the conformal factor of the metric.

Contribution

It demonstrates that the form of the conformal factor in 4D metrics derived from 5D vacuum solutions determines the matter equation of state in cosmological models.

Findings

The conformal factor influences the matter equation of state.

Different equations of state are analyzed for flat, open, and closed models.

The G(55) component of the 5D metric simulates matter in the 4D models.

Abstract

4-dimensional homogeneous isotropic cosmological models obtained from solutions of vacuum 5-dimensional Einstein equations are considered. It is assumed, that the G(55)-component of the 5-d metric simulates matter in the comoving frame of reference. Observable 4-d metric is defined up to conformal transformations of the metric of 4-d section \tilde{g}, with a conformal factor as a function of the component G(55). It is demonstrated, that the form of this function determines the matter equation of state. Possible equations of state are analyzed separately for flat, open and close models.