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arXiv · 1212.3201

Isotropy theorem for cosmological Yang-Mills theories

J. A. R. Cembranos·A. L. Maroto·S. J. Núñez Jareño
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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 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 fields is always isotropic and has the perfect fluid form for any locally inertial observer.

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J. A. R. Cembranos, A. L. Maroto, S. J. Núñez Jareño. 2013-03-05. Isotropy theorem for cosmological Yang-Mills theories. https://doi.org/10.1103/physrevd.87.043523

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