Topology and models of ZFC at early Universe

Main Article Content

Jerzy Król
Torsten Asselmeyer-Maluga

Abstract

Recently the cosmological evolution of the universe has been considered where 3-dimensional spatial topology undergone drastic changes. The process can explain, among others, the observed smallness of the neutrino masses and the speed of inflation. However, the entire evolution is perfectly smooth from 4-dimensional point of view. Thus the raison d’être for such topology changes is the existence of certain non-standard 4-smoothness on R4 already at very early stages of the universe. We show that the existence of such smoothness can be understood as a byproduct of the quantumness of the origins of the universe. Our analysis is based on certain formal aspects of the quantum mechanical lattice of projections of infinite dimensional Hilbert spaces where formalization reaches the level of models of axiomatic set theory.

Article Details

Section
Emergence of the Classical

References

Asselmeyer-Maluga, T. and Król, J., 2014. Inflation and topological phase transition driven by exotic smoothness. Advances in High Energy Physics [Online], 2014, pp.1–14. Available at: https://doi.org/10.1155/2014/867460 [Accessed 1 July 2019].

Asselmeyer-Maluga, T. and Król, J., 2018. How to obtain a cosmological constant from small exotic R4. Physics of the Dark Universe, 19, pp.66–77. Available at: https://doi.org/10.1016/j.dark.2017.12.002.

Asselmeyer-Maluga, T. and Król, J., 2019. A topological approach to neutrino masses by using exotic smoothness. Modern Physics Letters A, 34(13), p.1950097. Available at: https://doi.org/10.1142/S0217732319500974.

Bell, J., 2005. Set Theory: Boolean-Valued Models and Independence Proofs. Oxford: Clarendon Press.

Boos, W., 1996. Mathematical quantum theory I: Random ultrafilters as hidden variables. Synthese, 107(1), pp.83–143. Available at: https://doi.org/10.1007/BF00413903.

Freedman, M.H., 1979. A Fake S3 × R. Annals of Mathematics [Online], 110(2), pp.177–201. Available at: https://doi.org/10.2307/1971257 [Accessed 1 July 2019].

Gando, A. et al., 2016. Search for Majorana neutrinos near the inverted mass hierarchy region with KamLAND-Zen. Physical Review Letters, 117(8), p.082503. Available at: https://doi.org/10.1103/PhysRevLett.117.082503.

Gompf, R.E. and Stipsicz, A.I., 1999. 4-manifolds and Kirby calculus, Graduate studies in mathematics 20. Providence, RI: American Mathematical Society.

Harnois-Déraps, J., Waerbeke, L. van, Viola, M. and Heymans, C., 2015. Baryons, neutrinos, feedback and weak gravitational lensing. Monthly Notices of the Royal Astronomical Society [Online], 450(2), pp.1212–1223. Available at: https://doi.org/10.1093/mnras/stv646 [Accessed 1 July 2019].

Jech, T., 2003. Set theory: the third millennium edition, revised and expanded. 3rd ed., Springer Monographs in Mathematics. Berlin, Heidelberg: Springer-Verlag.

Jech, T., 1986. Multiple forcing, Cambridge Tracts in Mathematics 88. Cambridge: Cambridge University Press.

Kappos, D.A., 1969. Probability Algebras and Stochastic Spaces. New York: Elsevier. Available at: https://doi.org/10.1016/C2013-0-07403-8.

Król, J., Asselmeyer-Maluga, T., Bielas, K. and Klimasara, P., 2017. From Quantum to Cosmological Regime. The Role of Forcing and Exotic 4-Smoothness. Universe [Online], 3(2), p.31. Available at: https://doi.org/10.3390/universe3020031 [Accessed 1 July 2019].

Król, J., Klimasara, P., Bielas, K. and Asselmeyer-Maluga, T., 2017. Dimension 4: Quantum origins of spacetime smoothness. Acta Physica Polonica B [Online], 48, pp.2375–2380. Available at: [Accessed 21 May 2019].

Planck Collaboration et al., 2016. Planck 2015 results. XIII. Cosmological parameters. Astronomy & Astrophysics [Online], 594, A13. arXiv: 1502.01589 [astro-ph.CO]. Available at: https://doi.org/10.1051/0004-6361/201525830 [Accessed 1 July 2019].

Solovay, R., 1970. A Model of set theory in which every set of reals is Lebesgue measurable. Annales of Mathematics, 92(1), pp.1–56.

Weinberg, S., 2018. Essay: Half a Century of the Standard Model. Physical Review Letters, 121(22), p.220001. Available at: https://doi.org/10.1103/PhysRevLett.121.220001.

Woodard, R.P., 2014. Perturbative quantum gravity comes of age. International Journal of Modern Physics D, 23(09), p.1430020. Available at: https://doi.org/10.1142/S0218271814300201.