How to Avoid the Ambiguity in Applying the Copernican Principle for Cosmic Topology: Take the Observational Approach

It is often stated that homogeneity and isotropy of the Universe are assumptions of the almost Friedmann-Lema^itre (FL) model (the hot big bang model), inspired from the Copernican Principle. However, only local homogeneity and isotropy are required by the model: multiply connected almost FL models are locally homogeneous and isotropic, but they can be globally anisotropic and/or globally inhomogeneous. Toy models are used here to show how global anisotropy and/or global inhomogeneity of an almost FL model could be shown directly in observations. This approach may avoid having to make any assumptions regarding global anisotropy and inhomogeneity.Comment: 9 pages, 6 figures, accepted for Advances in Space Researc

Some spaces are more equal than others

It has generally been thought that in perturbed Friedmann-Lemaitre-Robertson-Walker models of the Universe, global topology should not have any feedback effects on dynamics. However, a weak-field limit heuristical argument, assuming a finite particle horizon for the transmission of gravitational signals, shows that a residual acceleration effect can occur. The nature of this effect differs algebraically between different constant curvature 3-manifolds. This potentially provides a selection mechanism for the 3-manifold of comoving space.Comment: 4 pages, proceedings of the Grassmannian Conference in Fundamental Cosmology, Szczecin, 14-19 Sep 2009, to be refereed by Annalen der Physi

On the possibility for constraining cosmic topology from the celestial distribution of astronomical objects

We present a method to constrain cosmic topology from the distribution of astronomical objects projected on the celestial sphere. This is an extension of the 3D method introduced in Fujii & Yoshii (2011) that is to search for a pair of pairs of observed objects (quadruplet) linked by a holonomy, i.e., the method we present here is to search for a pair of celestial sphere $n$-tuplets for $n \geq 3$. We find, however, that this method is impractical to apply in realistic situations due to the small signal to noise ratio. We conclude therefore that it is unrealistic to constrain the topology of the Universe from the celestial distribution, and the 3D catalogs are necessary for the purpose.Comment: 4 pages, 1 figure, accepted for publication in A&A (2011

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