Generalized non-commutative inflation
Abstract
Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f(E)\equiv \frac{E}{pc}({\ne} 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 et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007)021 and JCAP11(2007)013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the α family of curves f(E) = 1 + (λE)α. 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}). 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.
- Publication:
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Classical and Quantum Gravity
- Pub Date:
- March 2012
- DOI:
- 10.1088/0264-9381/29/6/065003
- arXiv:
- arXiv:1102.4828
- Bibcode:
- 2012CQGra..29f5003M
- Keywords:
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- Astrophysics - Cosmology and Extragalactic Astrophysics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
- E-Print:
- Final version considerably improved