Non-commutative geometry as a realization of varying speed of light cosmology
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 (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.
Keywords
Cite
@article{arxiv.hep-th/0104093,
title = {Non-commutative geometry as a realization of varying speed of light cosmology},
author = {Stephon H. S. Alexander and João Magueijo},
journal= {arXiv preprint arXiv:hep-th/0104093},
year = {2010}
}
Comments
11 pages, 7 figures (final version)