A Topological Model of the Universe: Klein Bottle and the Unification of the Big Crunch and Big Rip

Un modelo topológico del universo: la botella de Klein y la unificación del Big Crunch y el Big Rip

Alberto Rafael Roman Soltero

Universidad Vizcaya de las Américas Campus Piedras Negras 

ORCID 0000-0003-2228-684X

Recibido: 9 de noviembre de 2024 | Aceptado: 17 de noviembre de 2024 | Publicado en línea: 19 de noviembre de 2024 |

How to cite:

Roman-Soltero, A. R (2024). A Topological Model of the Universe: Klein Bottle and the Unification of the Big Crunch and Big Rip. Revista Multidisciplinaria de Ciencia Básica, Humanidades, Arte y Educación, 2(9), 24-32.

Abstract:

This paper presents a topological model of the universe based on the geometry of the Klein bottle, proposing that the Big Crunch and Big Rip may represent two manifestations of a single event within a non-orientable, cyclic universe. Using Roman’s Theorem of inverse permutations, which suggests symmetrical inverse states, the study explores how this topology may support a dynamic where cosmic expansion and collapse occur within a unified, cyclical framework. The model aims to reconcile certain anomalies observed in the Cosmic Microwave Background (CMB) and the distribution of dark matter by proposing a non-orientable spatial configuration. Preliminary findings suggest that a Klein bottle topology could align with Lambda Cold Dark Matter (ΛCDM) model observations, offering a novel perspective on cosmic evolution that connects expansion phases with contraction within a continuous topological cycle. The implications for dark energy, cosmic inflation, and the universe’s ultimate fate are discussed, emphasizing the model’s potential for expanding current cosmological paradigms.

Keywords: 

Klein bottle topology; Cyclic Universe; Big Crunch; Big Rip; Roman’s Theorem.

 

Descargar artículo

References:

Caldwell, R. R., Kamionkowski, M., & Weinberg, N. N. (2003). Phantom Energy: Dark Energy withw<−1Causes a Cosmic Doomsday. Physical Review Letters, 91(7). https://doi.org/10.1103/physrevlett.91.071301  

Carroll, S. (2010). From eternity to here the quest for the ultimate theory of time. Dutton.

Copi, C. J., Dragan Huterer, Schwarz, D. J., & Starkman, G. D. (2010). Large-Angle Anomalies in the CMB. Advances in Astronomy. Testing the Gaussianity and Statistical Isotropy of the Universe, 1–17. https://doi.org/10.1155/2010/847541  

Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen Der Physik, 354(7), 769–822. https://doi.org/10.1002/andp.19163540702  

Guth, A. H. (1981). Inflationary universe: A possible solution to the horizon and flatness problems. Physical Review D, 23(2), 347–356. https://doi.org/10.1103/physrevd.23.347  

Hawking, S. W. (1984). The quantum state of the universe. Nuclear Physics B, 239(1), 257–276. https://doi.org/10.1016/0550-3213(84)90093-2  

Hawking, S. W., & Ellis, G. F. R. (2023). The Large Scale Structure of Space-Time (50th Anniversary Edition). Cambridge University Press.

Hawking, S. W., & Page, D. N. (1983). Thermodynamics of black holes in anti-de Sitter space. Communications in Mathematical Physics, 87(4), 577–588. https://doi.org/10.1007/bf01208266  

Liddle, A. R. (2015). An introduction to modern cosmology. Wiley.

Nabila Aghanim, Yashar Akrami, Ashdown, M., J. Aumont, Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Basak, S., Battye, R. A., K. Benabed, Bernard, J., Bersanelli, M., Bielewicz, P., Bock, J. J., Bond, J. R., Borrill, J., Bouchet, F. R., & Boulanger, F. (2021). Planck 2018 results. Astronomy and Astrophysics, 652 (August 2021), C4–C4. https://doi.org/10.1051/0004-6361/201833910e  

Peebles, P. J. E., & Ratra, B. (2003). The cosmological constant and dark energy. Reviews of Modern Physics, 75(2), 559–606. https://doi.org/10.1103/revmodphys.75.559  

Penrose, R. (2011). Cycles of Time: An Extraordinary New View of the Universe. Knopf.

Roman-Soltero, A. R. (2024). Roman’s Theorem: Inverse Permutation on Extreme Values. Revista Multidisciplinaria de Ciencia Básica, Humanidades, Arte y Educación, 2(5), 47–53. https://doi.org/10.5281/zenodo.10871331  

Schwarz, D. J., Starkman, G. D., Huterer, D., & Copi, C. J. (2004). Is the Low-ℓ Microwave Background Cosmic? Physical Review Letters, 93(22). https://doi.org/10.1103/physrevlett.93.221301  

Spergel, D. N., Bean, R., Dore, O., Nolta, M. R., Bennett, C. L., Dunkley, J., Hinshaw, G., Jarosik, N., Komatsu, E., Page, L., Peiris, H. V., Verde, L., Halpern, M., Hill, R. S., Kogut, A., Limon, M., Meyer, S. S., Odegard, N., Tucker, G. S., & Weiland, J. L. (2007). Three‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Implications for Cosmology. The Astrophysical Journal Supplement Series, 170(2), 377–408. https://doi.org/10.1086/513700  

Steinhardt, P. J., & Turok, N. (2005). The cyclic model simplified. New Astronomy Reviews, 49(2-6), 43–57. https://doi.org/10.1016/j.newar.2005.01.003 

Tegmark, M., Strauss, M. A., Blanton, M. R., Abazajian, K., Dodelson, S., Sandvik, H., Wang, X., Weinberg, D. H., Zehavi, I., Bahcall, N. A., Hoyle, F., Schlegel, D., Scoccimarro, R., Vogeley, M. S., Berlind, A., Budavari, T., Connolly, A., Eisenstein, D. J., Finkbeiner, D., & Frieman, J. A. (2004). Cosmological parameters from SDSS and WMAP. Physical Review D, 69(10). https://doi.org/10.1103/physrevd.69.103501  

Weeks, J. R. (2020). The Shape of Space (3rd ed.). CRC Press.

Weinberg, S. (1972). Gravitation and cosmology: principles and applications of the general theory of relativity. Wiley.

Weinberg, S. (2008). Cosmology. Oxford University Press.