## Detectability of cosmic topology in almost flat universes |

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Page 12

If using a catalogue of cosmic objects with redshift cut-off up to zmax yields no

discarded as a model for the shape of our universe, while those with Tmax > 1 ...

If using a catalogue of cosmic objects with redshift cut-off up to zmax yields no

**multiple images**, then any lens space satisfying Tmax < 1 (rTMox < Xobs) can bediscarded as a model for the shape of our universe, while those with Tmax > 1 ...

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Table 4: Lens spaces L(p, q) with p > p* are discarded on the basis of

observations if there aje no

three different set of (fio , ^ao) in the bound (i). For a given universe [fixed (ft0 > ^

Au)] and for ...

Table 4: Lens spaces L(p, q) with p > p* are discarded on the basis of

observations if there aje no

**multiple images**up to zmax = 1 in universes withthree different set of (fio , ^ao) in the bound (i). For a given universe [fixed (ft0 > ^

Au)] and for ...

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3 also shows that if only quasars are used (redshift up to zmax = 6) and no

shape of our universe, as the corresponding solution curve lies above the current

bounds ...

3 also shows that if only quasars are used (redshift up to zmax = 6) and no

**multiple images**exist, then no hyperbolic manifolds can be excluded as theshape of our universe, as the corresponding solution curve lies above the current

bounds ...

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### Common terms and phrases

3-manifold 3-sphere astronomical survey bounds on cosmological catalogue with zmax closed geodesic CMBR compact manifold compact topologies concrete examples corresponding solution curve cosmic topology cosmological constant covering group covering space critical density curvature radius cyclic groups density parameters depth zmax detectability of cosmic exclude certain families families of possible families of topologies fimo FÍSICA fixed given manifold globally homogeneous horizon radius infinite number injectivity radius isometry lens space topologies Lens spaces L(p manifolds that remain maximal inradius r™ax multiple images multiply connected nearly flat FLRW nearly flat hyperbolic Nearly Flat Universes non-trivial topologies non-zero curvature non-zero lower bound observational bounds orientable hyperbolic manifolds possible topologies quasars question of detectability r,nj recent observations redshift cut-off remain undetectable rinj rmax shape smallest closed geodesies SnapPea spherical manifolds subset of lens Table topology of nearly total density undetectable and families undetectable topologies vacuum energy values of Xobs Xhor Xoba