Which FLRW comoving 3-manifold is preferred observationally and theoretically?

TL;DR

This paper evaluates observational and theoretical preferences for different FLRW comoving 3-manifolds, highlighting the Poincare dodecahedral space and 3-torus as leading candidates based on CMB data and residual gravity effects.

Contribution

It compares observational and theoretical criteria to determine the most favored FLRW 3-manifolds, emphasizing the Poincare space and flat spaces.

Findings

Residual gravity effect favors the Poincare space.

CMB observations favor compact FLRW models.

Measure space argument favors flat spaces almost surely.

Abstract

The lack of structure greater than 10 Gpc/h in Wilkinson Microwave Anisotropy Probe (WMAP) observations of the cosmic microwave background (CMB) favours compact Friedmann-Lemaitre-Robertson-Walker (FLRW) models of the Universe. The present best candidates based on observations are the Poincare dodecahedral space S^3/I^* and the 3-torus T^3. The residual gravity effect favours the Poincare space, while a measure space argument where the density parameter is a derived parameter favours flat spaces almost surely.