Publication: Isotropy theorem for cosmological Yang-Mills theories
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2013-02-13
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American Physical Society
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Abstract
We consider homogeneous non-Abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for an arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills field is always isotropic and has the perfect fluid form for any locally inertial observer.
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© 2013 American Physical Society.
We thank Marco Peloso and Jose Beltrán Jiménez for useful comments. This work has been supported by MICINN (Spain) project numbers FIS2011-23000, FPA2011-27853-01, and Consolider-Ingenio MULTIDARK CSD2009-00064.
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