Geometrical Order–of–magnitude Estimates for Spatial Curvature in Realistic Models of the Universe

The thoughts expressed in this article are based on remarks made by Jürgen Ehlers at the Albert– Einstein–Institut, Golm, Germany in July 2007. The main objective of this article is to demonstrate, in terms of plausible order–of–magnitude estimates for geometrical scalars, the relevance of spatial curvature in realistic models of the Universe that describe the dynamics of structure formation since the epoch of matter–radiation decoupling. We introduce these estimates with a commentary on the use of a quasi–Newtonian metric form in this context. PACS number(s): 04.20.-q, 04.20.Cv, 98.80.-k, 98.80.Jk Preprint number(s): arXiv:0906.0134 [gr-qc] DOI: 10.1007/s10714-009-0828-4 In Memoriam: Jürgen Ehlers (1929–2008)