Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

作     者：U. D. Machado R. Opher 

作者机构：Center for Radiophysics and Space Research Cornell University 613 Space Science Building Ithaca New York 14853 USA and Departamento de Astronomia Geofísica e Ciências Atmosféricas Universidade de São Paulo Rua do Matão 1226-Cidade Universitária-São Paulo São Paulo 05508-090 Brazil School of Electrical and Computer Engineering-Cornell University 428 Phillips Hall Ithaca New York 14853 USA and Departamento de Astronomia Geofísica e Ciências Atmosféricas Universidade de São Paulo Rua do Matão 1226-Cidade Universitária-São Paulo São Paulo 05508-090 Brazil 

出 版 物：《Physical Review D》 (物理学评论D辑：粒子、场、重力与宇宙学)

年 卷 期：2013年第87卷第12期

页      面：123517-123517页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 

基　　金：CNPq [142393/2006-1, 246020/2012-1] FAPESP [06/56213-9] Brazilian agency CNPq [300414/82-0] Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [06/56213-9] Funding Source: FAPESP 

主　　题：INFLATIONARY universe NONRELATIVISTIC quantum mechanics EQUATIONS of state REPRESENTATION theory (Algebra) GROUP theory VON Neumann algebras 

摘      要：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.