Zitat:
Zitat von Timm
Die hakt er schnell ab, denn er bevorzugt die triviale Topologie.
|
Warum?
Generell: die Friedmann-Modelle sind eine recht eingeschränkte Klasse von Lösungen; warum sollten gerade sie realisiert sein?
Keine nicht-triviale Topologie kann phänomenologisch ausgeschlossen werden, wenn das Universum nur genügend groß ist.
Die Geometrisierung von geschlossenen = kompakten und unberandeten 3-Mannigfaltigkeiten - vermutet von Thurston und bewiesen von Perelmann - führt auf eine endliche Menge “irreduzibler Typen” geschlossener Mannigfaltigkeit. Für nicht-kompakte hyperbolische 3-Mannigfaltigkeiten ist keine vollständige Klassifizierung bekannt.
https://en.wikipedia.org/wiki/Geometrization_conjecture
https://en.wikipedia.org/wiki/3-manifold
https://en.wikipedia.org/wiki/Flat_manifold
https://en.wikipedia.org/wiki/Homolo...omology_sphere
https://en.wikipedia.org/wiki/Mostow_rigidity_theorem
https://en.wikipedia.org/wiki/Hyperbolic_3-manifold
https://en.wikipedia.org/wiki/Pseudosphere
Anbei ein Auszug von
https://arxiv.org/abs/1601.03884
The Status of Cosmic Topology after Planck Data
Jean-Pierre Luminet
(Submitted on 15 Jan 2016 (v1), last revised 17 Mar 2016 (this version, v2))
In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply-connected or multi-connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi-connected small universe models is to create multiples images of faraway cosmic sources.
While the last CMB (Planck) data fit well the simplest model of a zero-curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincare Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. We review the theoretical and observational status of the field.
One could think that the whole universe is necessarily greater than the observable one, as it would obviously be the case if space was infinite, for instance the simply-connected flat or hyperbolic space. Then the observable universe would be an infinitesimal patch of the whole universe and, although it has long been the standard “mantra” of many theoretical cosmologists,
this is not and will never be a testable hypothesis.
The whole universe can also be finite (without an edge), e.g., a hypersphere or a closed multi-connected space, but greater than the observable universe. In that case, one easily figures out that
if whole space widely encompasses the observable one, no signature of its finiteness will show in the experimental data.
Surprisingly enough, the whole space could be
smaller than the observable universe, due to the fact that space can be both multi-connected, have a small volume and produce topological lensing.
This is the only case where there are a lot of testable possibilities, whatever the curvature of space.
The present observational constraints on the Ω° parameter favor a spatial geometry that is nearly flat with a 0.4% margin of error. Note that the constraints on the curvature parameter can be looser if we consider a general form of dark energy (not the cosmological constant), which leaves rooms to consider positively or negatively curved cosmological models that are usually regarded as being excluded. However,
even with the curvature so severely constrained by cosmological data, there are still possible multi-connected topologies that support positively curved, negatively curved, or flat metrics.
Even if particularly simple and elegant models such as the PDS and the hypertorus
are now claimed to be ruled out at a subhorizon scale,
many more complex models of multi-connected space cannot be eliminated as such.
Zusammenfassend: nicht-triviale Topologien mit typischen Längenskalen im Bereich der Größe des sichtbaren Universums sind weiterhin nicht vollständig ausgeschlossen; nicht-triviale Topologien mit typischen Längenskalen deutlich größer als das sichtbare Universums können prinzipiell nicht - nie - ausgeschlossen werden.