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Universe 2017, 3(2), 31; doi:10.3390/universe3020031

From Quantum to Cosmological Regime. The Role of Forcing and Exotic 4-Smoothness

1
Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland
2
German Aerospace Center, Rutherfordstraße 2, 12489 Berlin, Germany
*
Author to whom correspondence should be addressed.
Academic Editors: Mariusz P. Dąbrowski, Manuel Krämer and Vincenzo Salzano
Received: 30 January 2017 / Revised: 5 March 2017 / Accepted: 21 March 2017 / Published: 27 March 2017
(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)
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Abstract

Recently, a cosmological model based on smooth open 4-manifolds admitting non-standard smoothness structures was proposed. The manifolds are exotic versions of R 4 and S 3 × R . The model has been developed further and proven to be capable of obtaining some realistic cosmological parameters from these exotic smoothings. The important problem of the quantum origins of the exotic smoothness of space-time is addressed here. It is shown that the algebraic structure of the quantum-mechanical lattice of projections enforces exotic smoothness on R n . Since the only possibility for such a structure is exotic R 4 , it is found to be a reasonable explanation of the large-scale four-dimensionality of space-time. This is based on our recent research indicating the role of set-theoretic forcing in quantum mechanics. In particular, it is shown that a distributive lattice of projections implies the standard smooth structure on R 4 . Two examples of models valid for cosmology are discussed. The important result that the cosmological constant can be identified with the constant curvature of the embedding ( exotic R 4 ) R 4 is referred. . The calculations are in good agreement with the observed small value of the dark energy density. View Full-Text
Keywords: cosmology and lattice of projections in QM; forcing; exotic 4-smoothness; cosmological constant cosmology and lattice of projections in QM; forcing; exotic 4-smoothness; cosmological constant
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Król, J.; Asselmeyer-Maluga, T.; Bielas, K.; Klimasara, P. From Quantum to Cosmological Regime. The Role of Forcing and Exotic 4-Smoothness. Universe 2017, 3, 31.

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