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

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.Comment: 3 pages, Twelfth Marcel Grossmann Meeting on General Relativity, ed. Thibault Damour, Robert T Jantzen, Remo Ruffini, Singapore: World Scientifi

A residual acceleration effect due to an inhomogeneity

The perturbed Friedmann-Lemaitre-Robertson-Walker models allow many different possibilities for the 3-manifold of the comoving spatial section of the Universe. It used to be thought that global properties of the spatial section, including the topology of the space, have no feedback effect on dynamics. However, an elementary, weak-limit calculation shows that in the presence of a density perturbation, a gravitational feedback effect that is algebraically similar to dark energy does exist. Moreover, the effect differs between different 3-spaces. Among the well-proportioned spaces, the effect disappears down to third order in several cases, and down to fifth order for the Poincare dodecahedral space S^3/I^*. The Poincare space, that which also is preferred in many observational analyses, is better-balanced than the other spaces.Comment: 6 pages, 1 figure, v1 submitted to Proceedings of the Invisible Universe International Conference, held in Paris, France, June 29-July 3, 2009 - after it is published, it will be found at http://proceedings.aip.org/proceedings

Observational Approaches to the Topology of the Universe

Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.Comment: very compact, (2 page) write-up of invited review for Marcel Grossmann IX Meeting in Roma, 1st page classifies and cites different observational strategies, 2nd page reference list includes many key 1999/2000 reference

Topological acceleration in relativistic cosmology

Heuristic approaches in cosmology bypass more difficult calculations that would more strictly agree with the standard Einstein equation. These give us the well-known Friedmann-Lemaitre-Robertson-Walker (FLRW) models, and, more recently, the feedback effect of the global topology of spatial sections on the acceleration of test particles. Forcing the FLRW heuristic model on observations leads to dark energy, which, pending fully relativistic calculations, is best interpreted as an artefact. Could topological acceleration also be an artefact of using a heuristic approach? A multiply connected exact solution of the Einstein equation shows that topological acceleration is present in at least one fully relativistic case---it is not an artefact of Newtonian-like thinking.Comment: 4 pages, 1 figure, Multiverse and Fundamental Cosmology Conference, 10-14 September, 2012, Szczecin, Polan