1211.6478 (U. D. Machado et al.)

A conceptual problem for non-commutative inflation and the new approach
for non-relativistic inflationary equation of state    [PDF]

U. D. Machado, R. Opher

In a previous paper, we connected the phenomenological non-commutative inflation of Alexander, Brandenberger and Magueijo (2003, 2005 and 2007) with the formal representation theory of groups and algebras. In that paper, the fundamental equations of inflation followed as a consequence of a deformation of the Poincar\'e group, which induces a particular quantum representation. 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 and that the procedure to obtain those equations should be modified according to one of two possible proposals. One of them relates to the general theory of Hopf algebras. The other is based on a representation theorem of Von Neumann algebras, a proposal already suggested by us to take into account interactions in the inflationary equation of state. This reopens the problem of finding inflationary deformed dispersion relations and all developments which followed the first paper of Non-commutative Inflation.

View original: http://arxiv.org/abs/1211.6478