Isotropy theorem for cosmological Yang-Mills theories

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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.
© 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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[1] L. H. Ford, Phys. Rev. D 40, 967 (1989). [2] C. Armendariz-Picon, J. Cosmol. Astropart. Phys. 07 (2004) 007. [3] C. G. Boehmer and T. Harko, Eur. Phys. J. C 50, 423 (2007). [4] T. Koivisto and D. F. Mota, J. Cosmol. Astropart. Phys. 08 (2008) 021; K. Bamba, S. ’i. Nojiri, and S. D. Odintsov, Phys. Rev. D 77, 123532 (2008). [5] B. Himmetoglu, C. R. Contaldi, and M. Peloso, Phys. Rev. Lett. 102, 111301 (2009); A. E. Gumrukcuoglu, B. Himmmetoglu, and M. Peloso, Phys. Rev. D 81, 063528 (2010). [6] J. B. Jimenez and A. L. Maroto, Phys. Rev. D 78, 063005 (2008); J. Cosmol. Astropart. Phys. 03 (2009) 016; Phys. Lett. B 686, 175 (2010); E. Carlesi, A. Knebe, G. Yepes, S. Gottloeber, J. B. Jimenez, and A. L. Maroto, Mon. Not. R. Astron. Soc. 418, 2715 (2011). [7] K. Dimopoulos, Phys. Rev. D 74, 083502 (2006). [8] A. E. Nelson and J. Scholtz, Phys. Rev. D 84, 103501 (2011). [9] A. Golovnev, V. Mukhanov, and V. Vanchurin, J. Cosmol. Astropart. Phys. 06 (2008) 009. [10] A. Maleknejad, M. M. Sheikh-Jabbari, and J. Soda, arXiv:1212.2921 [11] K. Yamamoto, M.-a. Watanabe, and J. Soda, Classical Quantum Gravity 29, 145008 (2012); M.-a. Watanabe, S. Kanno, and J. Soda, Phys. Rev. Lett. 102, 191302 (2009); K. Murata and J. Soda, J. Cosmol. Astropart. Phys. 06 (2011) 037; A. Maleknejad and M. M. Sheikh-Jabbari, Phys. Rev. D 85, 123508 (2012). [12] J. Cervero and L. Jacobs, Phys. Lett. 78B, 427 (1978); M. Henneaux, J. Math. Phys. (N.Y.) 23, 830 (1982); Y. Hosotani, Phys. Lett. 147B, 44 (1984). [13] D.V. Galtsov and M. S. Volkov, Phys. Lett. B 256, 17 (1991); D.V. Gal’tsov, arXiv:0901.0115. [14] Y. Zhang, Phys. Lett. B 340, 18 (1994); Classical Quantum Gravity 13, 2145 (1996); E. Elizalde, CEMBRANOS, MAROTO, AND JAREN˜ O PHYSICAL REVIEW D 87, 043523 (2013) A. J. Lopez-Revelles, S. D. Odintsov, and S.Y. Vernov, arXiv:1201.4302. [15] J. A. R. Cembranos, C. Hallabrin, A. L. Maroto, and S. J. Núñez Jareño, Phys. Rev. D 86, 021301 (2012). [16] A. Maleknejad and M. M. Sheikh-Jabbari, arXiv:1102.1513; Phys. Rev. D 84, 043515 (2011); P. Adshead and M. Wyman, Phys. Rev. Lett. 108, 261302 (2012); Phys. Rev. D 86, 043530 (2012); K. Yamamoto, Phys. Rev. D 85, 123504 (2012); M.M. Sheikh-Jabbari, Phys. Lett. B 717, 6 (2012); A. Ghalee, Phys. Lett. B 717, 307 (2012); M. Noorbala and M. M. Sheikh-Jabbari, arXiv:1208.2807; K.-i. Maeda and K. Yamamoto arXiv:1210.4054; E. Dimastrogiovanni, M. Fasiello, and A. J. Tolley, arXiv:1211.1396. [17] R. Ticciati, Quantum Field Theory for Mathematicians (Cambridge University Press, Cambridge, 1999); M. E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Boulder, CO, 1995). [18] M. S. Turner, Phys. Rev. D 28, 6 (1983). [19] C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980). [20] A. Z. Petrov, Einstein Spaces (Pergamon, Oxford, 1969). [21] N. Bartolo, S. Matarrese, M. Peloso, and A. Ricciardone, Phys. Rev. D 87, 023504 (2013).