New approaches to cosmological models, based on geometric and topological principles, may allow alternative interpretations for the dark content of the Universe and the inflation paradigm. In this work we use a cusp hyperbolic space glued to singular points of Seifert Fibered homologic spheres in order to avoid the cosmological point-like singularities (only in the glued parts). We show that some results of this approach can reproduce accurate, at least in terms of the hierarchy, recent measurements in experimental physics and observational cosmology. From the proposed infinite space with finite volume, we calculate the equivalent values for fundamental coupling constants in our current time for an alternative singularity-free Universe.

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