TITLE:
Local and Global Flatness in Cosmology
AUTHORS:
Rainer Burghardt
KEYWORDS:
Curvature Parameter, Bianchi Identities, de Sitter Cosmos, Subluminal Cosmos, Rh=ct Cosmos, Geometric Horizon
JOURNAL NAME:
Journal of Modern Physics,
Vol.10 No.12,
November
5,
2019
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 Rh=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.