Hamilton (Jacobi) formulation of the dark sector of the universe and contextualize...
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Cornell Univ, Ctr Radiophys & Space Res, Ithaca, NY 14853 - USA
[2] Univ Sao Paulo, Dept Astron & Geofis & Ciencias Atmosfer, BR-05508090 Sao Paulo - Brazil
[3] Cornell Univ, Sch Elect & Comp Engn, Ithaca, NY 14853 - USA
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Physical Review D; v. 87, n. 12 JUN 17 2013. |
| Web of Science Citations: | 1 |
| Abstract | |
In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo {[}Phys. Rev. D 67, 081301 (2003)] and Koh and Brandenberger {[}J. Cosmol. Astropart Phys. 06 (2007) 21] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state. (AU) | |
| FAPESP's process: | 06/56213-9 - New physics from space: formation and evolution of structures in the universe |
| Grantee: | Claudia Lucia Mendes de Oliveira |
| Support type: | Research Projects - Thematic Grants |