Re-evaluation of $Ω_k$ of the normalised Friedmann-Lema\^ıtre-Robertson-Walker model: Implications for Hubble constant determinations

Abstract

The description of spacetime is an fundamental problem of cosmology. We explain why the current assignments of spacetime geometries for Ω k of the Friedmann-Lemaître-Robertson-Walker (FLRW) model are probably incorrect and suggest more useful descriptions. We show that Ω k represents not only curvature but the influence of matter density on the extent of spacetime between massive objects. Recent analyses of supernovae type Ia (SNe Ia) and HII/GEHR data with the FLRW model present the best fits with a small value for Ω m and a large Ω k . These results are consistent with our Universe exhibiting sparse matter density and quasi-Euclidean geometry and the small Ω m value agrees with Big Bang nucleosynthesis calculations. We suggest the geometry of our current Universe is better described by a value for Ω k ≈1 rather than 0. As an example we extend the FLRW model towards the Big Bang and discover a simple explanation of how matter creation developed into the currently geometrically flat Universe with sparse, homogeneous, isotropic matter and energy distributions.Assigning Ω k ≈ 1 to describe quasi-Euclidean spacetime geometry is also useful for estimating H 0 and should help resolve the "tension" surrounding current estimates by different investigators.