### Non-commutative geometry as a realization of varying speed of light cosmologyNon-commutative geometry as a realization of varying speed of light cosmology

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 Author Alexander, Stephon H. S. ♦ Magueijo, João Source arXiv.org Content type Text File Format PDF Date of Submission 2001-04-10 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Astronomy & allied sciences ♦ Physics Subject Keyword High Energy Physics - Theory ♦ Astrophysics ♦ General Relativity and Quantum Cosmology ♦ High Energy Physics - Phenomenology ♦ physics:astro-ph ♦ physics:gr-qc ♦ physics:hep-ph ♦ physics:hep-th Abstract We examine the cosmological implications of space-time non-commutativity, discovering yet another realization of the varying speed of light model. Our starting point is the well-known fact that non-commutativity leads to deformed dispersion relations, relating energy and momentum, implying a frequency dependent speed of light. A Hot Big Bang Universe therefore experiences a higher speed of light as it gets hotter. We study the statistical physics of this "deformed radiation", recovering standard results at low temperatures, but a number of novelties at high temperatures: a deformed Planck's spectrum, a temperature dependent equation of state $w=p/\rho$ (ranging from 1/3 to infinity), a new Stephan-Boltzmann law, and a new entropy relation. These new photon properties closely mimic those of phonons in crystals, hardly a surprising analogy. They combine to solve the horizon and flatness problems, explaining also the large entropy of the Universe. We also show how one would find a direct imprint of non-commutativity in the spectrum of a cosmic graviton background, should it ever be detected. Description Reference: Proceedings of the XIIIrd Rencontres de Blois, pp281, 2004 Educational Use Research Learning Resource Type Article Page Count 11