simple connectedness: Shrink an embedded ball (solid down to a patch of 3-manifold (positive definite scale in SRM), or down to infinitesimal (i.e. element of set) for Cs_m scale i.e. < Planck scale. Hence consistent with no handles, singularities, nor other multi-connectedness such as wormholes. Thus would such regional volume V_R 3-manifold's alleged simple connectedness, together with Poincare’s conjecture, suggest that no other 3-manifold topology, other than 3-sphere, would seem suitable, for the shape of our ‘universe’? This would be in counter-distinction to Big Bang, which would seem to have some asymmetry (anisotropy) based on CMB asymmetry of 10^-5; and more so for nucleosynthesis for first 90 seconds?
Such CMB asymmetry suggests a greater asymmetry (anisotropy) for earlier Big Bang, since such radiation has been mixing for a long time in 3-volume, wherein latter has been expanding much slower, assuming such Hubble parameter is proportional to LSS (~640 km/s) of our Local Group to CMB; both LSS and Hubble expansion allegedly are considered modified global interdependent variables.
So might our ‘universe’ 3-volume seem to be a perfect 3-sphere in comparison to asymmetry (and heterogeneity?) of Big Bang nucleosynthesis? Hence suggestive of a mechanistic dissimularity of the two concomitant unfolding events; one local differentiation on a manifold, while the other on modified global scale? Also one has a local gauge description, while the other is a global gauge description.
Might one consider a scenario of s^3 serving as a broader array of objects suitable for the shape of ‘universe’? That is could different shapes, such as ink blot, be homotopic to 3-sphere; hence suitable for shape of ‘universe’? However physically then one would have anisotropy to magnitude of Hubble parameter, in principle. In contrast in SRM model, Hubble expansion is considered a modified global interdependent variable; changing together with all other such MTCs (modified time constructs). Thus 3-sphere, rather than s^3 , would seem more suitable for shape of ‘universe’.
Could one consider a dodecahedron for the shape of universe? But radius from geometric center to vertices, versus mid-point of a face, would differ; hence anisotropy to Hubble expansion and changing Hubble parameter.
anisotropy of universe?