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 h R 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.

White Hole Cosmology - One Best Alternative for Standard Cosmology

“…In this context, it is very important to consider R. Burghardt's model [61,62] of 'Subluminal universe' having a positive curvature and light speed expansion. It resembles Melia's model [15,63,64,65] of the universe in all respects and deviates from 'Flat model'.…”

Melia’s R<sub>h</sub> = ct Model Is by No Means Flat

“…In the following section, we will demonstrate step by step that Melia's R h = ct model is not flat at all. We have referred to our earlier papers [2] [3] where we treated the same aspect of the problem. Here, we have summarized the results.…”