Local and Global Flatness in Cosmology

Abstract

We raise the question of how the curvature parameter k is related to the curvature of the universe. We also show that, for a cosmological model that can be interpreted geometrically as a pseudo-hypersphere with a time-dependent radius, the Einstein field equations are not sufficient to fully describe the model. In addition, the differential equation system of Bianchi identities is required to describe the temporal evolution of the universe. We discuss the facts using the example of the de Sitter universe, the subluminal universe and the R h =ct model by Melia. In particular, we discuss the formal differences between the two latter models and claim that both models are identical. We also examine the possibility of introducing non-comoving coordinates.