Physics NotePublished
What do very nearly flat detectable cosmic topologies look like?
Bruno Mota; G.I. Gomero; Marcelo José Rebouças; R. Tavakol
2003
Publication details
- Authors
- Bruno Mota; G.I. Gomero; Marcelo José Rebouças; R. Tavakol
- Type
- Physics Note
- Status
- Published
- Publication date
- 2003
- Description
- Recent studies of the detectability of cosmic topology of nearly flat universes have often concentrated on the range of values of $\Omega_{0}$ given by current observations. Here we study the consequences of taking a range of bounds satisfying $|\Omega_0 - 1| \ll 1$, which include those expected from future observations such as the Planck mission, as well those predicted by inflationary models. We show that in this limit, a generic detectable non-flat manifold is locally indistinguishable from either a cylindrical ($\mathbb{R}^2 \times \mathbb{S}^1$) or toroidal ($\mathbb{R} \times \mathbb{T}^2$) manifold, irrespective of its global shape, with the former being more likely. Importantly this is compatible with some recent indications based on the analysis of high resolution CMB data. It also implies that in this limit an observer would not be able to distinguish topologically whether the universe is spherical, hyperbolic or flat. By severely restricting the expected topological signatures of detectable isometries, our results provide an effective theoretical framework for interpreting cosmological observations, and can be used to confine any parameter space which realistic search strategies, such as the `circles in the sky' method, need to concentrate on.
- Year
- 2003
- Number
- CBPF-NF-039/03
- Linked to a thesis
- No
- Linked to a grant
- No