English

Generalized Non-Commutative Inflation

Cosmology and Nongalactic Astrophysics 2012-02-27 v4 General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics math.MP

Abstract

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f(E)Epc(1)f(E)\equiv\frac{E}{pc}(\neq 1) 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 α\alpha family of curves f(E)=1+(λE)αf(E)=1+(\lambda E)^{\alpha}. 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 SL(2,C)SL(2,\mathbb{C}). 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.

Keywords

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

R2 v1 2026-06-21T17:30:47.500Z