FRW universe models in conformally flat-spacetime coordinates III: Universe models with positive spatial curvature

摘要

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 Lorentz Invariant Vacuum Energy (LIVE)-dominated universe when conformal time is used in Friedmann-Robertson-Walker (FRW) 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.