## Detectability of cosmic topology in almost flat universes |

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We find that given the present bounds on cosmological parameters, there are

families of both hyperbolic and spherical manifolds that

families that can be excluded as the shape of our universe. These results are of

importance in future search strategies for the detection of the shape of our

universe, given that there are an infinite number of theoretically possible

topologies and that the future observations are expected to put a non-zero lower

bound on |fto — 1| ...

We find that given the present bounds on cosmological parameters, there are

families of both hyperbolic and spherical manifolds that

**remain undetectable**andfamilies that can be excluded as the shape of our universe. These results are of

importance in future search strategies for the detection of the shape of our

universe, given that there are an infinite number of theoretically possible

topologies and that the future observations are expected to put a non-zero lower

bound on |fto — 1| ...

Page 11

Thus using quasars, the topology of the five known smallest hyperbolic manifolds

, as well as m009(4,l), are undetectable within the hyperbolic region of the

parameter space given by (ii), while only topologies m007(3,l) and m009(4,l)

used T,nj together with observational bounds on cosmological parameters in

order to set bounds on detectability. We shall now employ the indicator Tmax as

a way of excluding ...

Thus using quasars, the topology of the five known smallest hyperbolic manifolds

, as well as m009(4,l), are undetectable within the hyperbolic region of the

parameter space given by (ii), while only topologies m007(3,l) and m009(4,l)

**remain undetectable**even if CMBR observations are used. Hitherto we haveused T,nj together with observational bounds on cosmological parameters in

order to set bounds on detectability. We shall now employ the indicator Tmax as

a way of excluding ...

Page 14

Considering concrete examples of both spherical and hyperbolic manifolds, we

find that, given the present observaional bounds on cosmological parameters,

there are families of both hyperbolic and spherical manifolds that

also demonstrate the importance of considering families of possible topologies,

rather than arbitrary individual examples, in search strategies for the detection of

the shape of ...

Considering concrete examples of both spherical and hyperbolic manifolds, we

find that, given the present observaional bounds on cosmological parameters,

there are families of both hyperbolic and spherical manifolds that

**remain****undetectable**and families that can be excluded as the shape of our universe. Wealso demonstrate the importance of considering families of possible topologies,

rather than arbitrary individual examples, in search strategies for the detection of

the shape of ...

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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