FRW Universe Models in Conformally Flat Spacetime Coordinates. III: Universe models with positive spatial curvature

TL;DR

This paper derives general expressions for positively curved universe models in conformally flat coordinates, analyzing their properties, horizons, and evolution with dust, radiation, and vacuum energy.

Contribution

It provides a comprehensive framework for modeling positively curved universes in conformally flat coordinates, including methods for horizon analysis and coordinate transformations.

Findings

Continual annihilation of space, matter, and energy in dust and radiation universes.

Continual creation of space, matter, and energy in vacuum energy-dominated universes.

Calculated age and redshift of models using conformal time.

Abstract

We deduce general expressions for the line element of universe models with positive spatial curvature described by conformally flat spacetime coordinates. Models with dust, radiation and vacuum energy are exhibited. Discussing the existence of particle horizons we show that there is continual annihilation of space, matter and energy in a dust and radiation dominated universe, and continual creation in a LIVE domined universe when conformal time is used in Friedmann-Robertson-Walker models with positive spatial curvature. A general procedure is given for finding coordinates to be used in Penrose diagrams. We also calculate the age and the redshift of some universe models using conformal time.