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Computing Hierarchical Cosmological Coupling Constants from an Alternative Seifert-Hyperbolic Approach

doi: 10.6062/jcis.2014.05.01.0081


M. E. Mejia, C. A. Caretta, D. H. Stalder, R. R. Rosa


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.


Topology, Cosmology, Thurston ́s theory, Singularity-Free


[1] A. Einstein Kosmologische Betrachtungen zur allgem einen Relativitatstheorie. Sitzungsber. K. Preuss. Akad. Wiss. 142-152. English translation in H.A. Lorentz, et al., eds. 1952. The Principle of Relativity. Dover Publications, Mineola, New York, 175-188. (1917).

[2] E. Hubble A Relation between Distance and Radial Velocity among Extra Galactic Nebulae. Proceedings of the National Academy of Sciences. Vol. 15. No. 3. 168-173. (1929).

[3] A. G. Riess, A. V. Filippenko, V. Alexei, P. Challis, A. Clocchiatti, A.Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, J. Tonry. Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, Vol. 116, No. 3, 1009-1038. (1998).

[4] A. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon , P. Ruiz Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. Newberg, W. J. Couch, and The Supernova Cosmology Project. Measurements of Omega and Lambda from 42 High-Redshift Supernovae. The Astrophysical Journal, Vol. 517, No. 2, 517-565. (1999).

[5] V. N. Efremov. Flat Connection Contribution to Topology Changing Amplitudes in an Ensemble of Seifert Fibered Homology Spheres. International Journal of Theoretical Physics, Vol. 35, No. 1, 63-85. (1996).

[6] V. N. Efremov. Siebenman-Type Cobordisms with Borders and Topology Changes by Quantum Tunneling. International Journal of Theoretical Physics. Vol. 36. No. 5, 1133-1151. (1997).

[7] V. N. Efremov and N. V. Mitskievitch. Discrete model of spacetime in terms of inverse spectra of the T0 Alexandroff topological spaces; e-print, arXivgr-qc \ 0301063.

[8] V. N. Efremov and N. V. Mitskievitch. Topology Changes in Terms of Proper Inverse Spectra of T0−Discrete Spaces and Hierarchy of Fundamental Interactions in a Universe Glued Together of Seifert Homologic Spheres. in: Progress in General Relativity and Quantum Cosmology Research, Nova Sci. Publishers. (2004).

[9] M. E. Mejia. R. R. Rosa An Alternative Manifold for Cosmology using Seifert Fibered and Hyperbolic Spaces. Applied Mathematics, Vol. 5, 1013-1028. (2014)

[10] Lopes, PAA; de Carvalho, RR; Kohl-Moreira, JL; Jones, C; 2009, MNRAS, 392, 135

[11] V. N. Efremov, N. V. Mitskievitch, A. M. Hernandes, R. Serrano. ́ Topological gravity on plumbed V-cobordisms. Class.Quant.Grav. Vol. 22, 3725-3744. (2005).

[12] J. Milnor. A unique decomposition theorem for 3-manifolds. American Journal of Math. Vol. 84, 1-7. (1962).

[13] D. Eisenbud and W. D. Newmann. Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. Annals of Mathematics Studies. University Press. (1985).

[14] K. Johanson. Homotopy equivalences of 3-manifolds with boundaries. Lecture Notes in Mathematics, 761. Springer, Berlin, N-Y. (1979).

[15] W. Jaco and P. B. Shalen. Seifert fibered spaces in 3-manifolds. Mem. Amer. Math. Soc. Vol. 21, No. 220. (1979).

[16] W. P. Thurston. Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. American Mathematical Society. Bulletin. New Series 6, No. 3, 357-381. (1982).

[17] W. P. Thurston. The Geometry and Topology of 3-Manifolds. Electronic version 1.0 . http://library.msri.org/books/gt3m/. (October 1997)

[18] W. P. Thurston. Three-Dimensional Geometry and Topology. Princeton University Press. Vol. 1. (1997).

[19] W. Jaco. Lectures on 3-Manifold Topology. Regional Conference Series in Mathematics. American Mathematical Society. (1980).

[20] J. Milnor. On the 3-dimensional Brieskorn Manifolds M(p,q,r). http://www.maths.ed.ac.uk/ ̃aar/papers /milnbries.pdf

[21] A. Mazumdar. New Developments on Embedding Inflation in Gauge Theory and Particle Physics. arXiv:0707.3350v1. (2007).

[22] J. A. Peacock Cosmological Physics. Cambridge Univ. Press. (1999).

[23] J. D. Barrow and D. J. Shaw. The value of the cosmological constant. General Relativity and Gravitation, Vol. 43, No. 10, 2555-2560. (2011).

[24] Q. Mason, H. D. Trottier, C. T. Davies, K. Foley, A. Gray, G. P. Lepage, from Realistic M. Nobes, J. Shigemitsu. Accurate Determinations of αs Lattice QCD. Phys.Rev.Lett. Vol. 95. (2005).

[25] P. J. Mohr, B. N. Taylor, D. B. Newell. CODATA Recommended Values of the Fundamental Physical Constants: 2010. Rev. Mod. Phys. Vol. 84, 1527-1605. (2012).

[26] W. D. Newmann and D. Zagier. Volumes of Hyperbolic Three-Manifolds. Topology. Vol. 24, No. 3, 307−332. (1985).


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