TITLE:
An Alternative Manifold for Cosmology Using Seifert Fibered and Hyperbolic Spaces
AUTHORS:
Maria E. Mejía, Reinaldo R. Rosa
KEYWORDS:
Topology, Cosmology, Thurston’s Theory, Singularity-Free
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.6,
April
8,
2014
ABSTRACT:
We propose a model with
3-dimensional spatial sections, constructed from hyperbolic cusp space glued to
Seifert manifolds which are in this case homology spheres. The topological part
of this research is based on Thurston’s conjecture which states that any
3-dimensional manifold has a canonical decomposition into parts, each of which
has a particular geometric structure. In our case, each part is either a
Seifert fibered or a cusp hyperbolic space. In our construction we remove tubular
neighbourhoods of singular orbits in areas of Seifert fibered manifolds using a
splice operation and replace each with a cusp hyperbolic space. We thus
achieve elimination of all singularities, which appear in the standard-like
cosmological models, replacing them by “a torus to infinity”. From this
construction, we propose an alternative manifold for cosmology with finite
volume and without Friedmann-like singularities. This manifold was used for
calculating coupling constants. Obtaining in this way a theoretical explanation
for fundamental forces is at least in the sense of the hierarchy.