Generalized Non-Commutative Inflation
Abstract
Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation for massless particles. This distorted energy-momentum relation can affect the radiation dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander, Brandenberger and Magueijo (2003, 2005 and 2007). These authors studied a one-parameter family of non-relativistic dispersion relation that leads to inflation: the family of curves . We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of . We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one parameter family of dispersion relations that lead to successful inflation.
Cite
@article{arxiv.1102.4828,
title = {Generalized Non-Commutative Inflation},
author = {U. D. Machado and R. Opher},
journal= {arXiv preprint arXiv:1102.4828},
year = {2012}
}
Comments
Final version considerably improved; Non-commutative inflation rigorously mathematically formulated