Gaugessence: a dark energy model with early time radiation-like equation of state

  • Ahmad Mehrabi
  • Azade Maleknejad
  • Vahid Kamali
Original Article


In this work, we study a new quintessence model associated with non-Abelian gauge fields, minimally coupled to Einstein gravity. This gauge theory has been recently introduced and studied as an inflationary model, called gauge-flation. Here, however, we are interested in the late time cosmology of the model in the presence of matter and radiation to explain the present time accelerating Universe. During the radiation and matter eras, the gauge field tracks radiation and basically acts like a dark radiation sector. As we approach lower redshifts, the dark component takes the form of a dark energy source which eventually becomes the dominate part of the energy budget of the Universe. Due to the tracking feature of our model, solutions with different initial values are attracted to a common trajectory. The existence of early dark radiation is a robust prediction of our model which contributes to the effective number of relativistic species, \(N_{eff}\) and has its own interesting observational features.


Gauge field Dark energy Observational data 



We thank the anonymous referee whose comments helped to improve the paper. In addition, we greatly appreciate M.M. Sheikh-Jabbari for his valuable comments on the manuscript. Work of A. Maleknejad is supported in part by the grant from Boniad Melli Nokhbegan of Iran. A. Maleknejad acknowledges the hospitality of the Aspen Center for Physics and support from PHY-1066293.


  1. Ackerman, L., Buckley, M.R., Carroll, S.M., Kamionkowski, M.: Proceedings, 7th International Heidelberg Conference on Dark Matter in Astro and Particle Physics (DARK 2009). Phys. Rev. D 79, 023519 (2009). arXiv:0810.5126 [hep-ph] ADSCrossRefGoogle Scholar
  2. Ade, P.A.R., et al. (Planck Collaboration): arXiv:1502.01589 [astro-ph.CO] (2015a)
  3. Ade, P., et al. (Planck Collaboration): arXiv:1502.01590 [astro-ph.CO] (2015b)
  4. Adshead, P., Wyman, M.: Phys. Rev. Lett. 108, 261302 (2012). arXiv:1202.2366 [hep-th] ADSCrossRefGoogle Scholar
  5. Amendola, L., et al. (Euclid Theory Working Group): Living Rev. Relativ. 16, 6 (2013). arXiv:1206.1225 [astro-ph.CO] ADSCrossRefGoogle Scholar
  6. Anderson, L., Aubourg, E., Bailey, S., Bizyaev, D., Blanton, M., et al.: Mon. Not. R. Astron. Soc. 427, 3435 (2013). arXiv:1203.6594 [astro-ph.CO] ADSCrossRefGoogle Scholar
  7. Aubourg, Ã., et al.: arXiv:1411.1074 [astro-ph.CO] (2014)
  8. Bamba, K., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 77, 123532 (2008). arXiv:0803.3384 [hep-th] ADSCrossRefGoogle Scholar
  9. Bassett, B.A., Hlozek, R.: arXiv:0910.5224 [astro-ph.CO] (2009)
  10. Baumann, D., Green, D., Meyers, J., Wallisch, B.: arXiv:1508.06342 [astro-ph.CO] (2015)
  11. Beutler, F., Blake, C., Colless, M., Jones, D.H., Staveley-Smith, L., et al.: Mon. Not. R. Astron. Soc. 416, 3017 (2011). arXiv:1106.3366 [astro-ph.CO] ADSCrossRefGoogle Scholar
  12. Bielefeld, J., Caldwell, R.R.: Phys. Rev. D 91, 124004 (2015). arXiv:1503.05222 [gr-qc] ADSCrossRefGoogle Scholar
  13. Blake, C., Kazin, E., Beutler, F., Davis, T., Parkinson, D., et al.: Mon. Not. R. Astron. Soc. 418, 1707 (2011). arXiv:1108.2635 [astro-ph.CO] ADSCrossRefGoogle Scholar
  14. Buen-Abad, M.A., Marques-Tavares, G., Schmaltz, M.: Phys. Rev. D 92, 023531 (2015). arXiv:1505.03542 [hep-ph] ADSCrossRefGoogle Scholar
  15. Carroll, S.M.: Living Rev. Relativ. 4, 1 (2001). arXiv:astro-ph/0004075 [astro-ph] ADSMathSciNetCrossRefGoogle Scholar
  16. Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Phys. Rep. 513, 1 (2012). arXiv:1106.2476 [astro-ph.CO] ADSMathSciNetCrossRefGoogle Scholar
  17. Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006). arXiv:hep-th/0603057 [hep-th] ADSCrossRefGoogle Scholar
  18. De Felice, A., Tsujikawa, S.: Living Rev. Relativ. 13, 3 (2010). arXiv:1002.4928 [gr-qc] ADSCrossRefGoogle Scholar
  19. Eisenstein, D.J., Hu, W.: Astrophys. J. 496, 605 (1998). arXiv:astro-ph/9709112 [astro-ph] ADSCrossRefGoogle Scholar
  20. Elizalde, E., Lopez-Revelles, A.J., Odintsov, S.D., Vernov, S.Yu.: Phys. At. Nucl. 76, 996 (2013). arXiv:1201.4302 [hep-th] CrossRefGoogle Scholar
  21. Follin, B., Knox, L., Millea, M., Pan, Z.: Phys. Rev. Lett. 115, 091301 (2015). arXiv:1503.07863 [astro-ph.CO] ADSCrossRefGoogle Scholar
  22. Foot, R., Vagnozzi, S.: Phys. Rev. D 91, 023512 (2015a). arXiv:1409.7174 [hep-ph] ADSCrossRefGoogle Scholar
  23. Foot, R., Vagnozzi, S.: Phys. Lett. B 748, 61 (2015b). arXiv:1412.0762 [hep-ph] ADSCrossRefGoogle Scholar
  24. Foot, R., Vagnozzi, S.: arXiv:1602.02467 [astro-ph.CO] (2016)
  25. Gal’tsov, D.V., Davydov, E.A.: Proc. Steklov Inst. Math. 272, 119 (2011). arXiv:1012.2861 [gr-qc]. doi: 10.1134/S0081543811010111. MathSciNetCrossRefGoogle Scholar
  26. Gross, C., Lebedev, O., Mambrini, Y.: J. High Energy Phys. 08, 158 (2015). arXiv:1505.07480 [hep-ph] CrossRefGoogle Scholar
  27. Gubitosi, G., Piazza, F., Vernizzi, F.: J. Cosmol. Astropart. Phys. 1302, 032 (2013). arXiv:1210.0201 [hep-th] ADSCrossRefGoogle Scholar
  28. Hinshaw, G., et al. (WMAP Collaboration): Astrophys. J. Suppl. 208, 19 (2013). arXiv:1212.5226 [astro-ph.CO] ADSCrossRefGoogle Scholar
  29. Hojjati, A., Linder, E.V.: arXiv:1507.08292 [astro-ph.CO] (2015)
  30. Hu, W., Sugiyama, N.: Astrophys. J. 471, 542 (1996). arXiv:astro-ph/9510117 [astro-ph] ADSCrossRefGoogle Scholar
  31. Huterer, D., et al.: Astropart. Phys. 63, 23 (2015). arXiv:1309.5385 [astro-ph.CO] ADSCrossRefGoogle Scholar
  32. Lesgourgues, J., Marques-Tavares, G., Schmaltz, M.: arXiv:1507.04351 [astro-ph.CO] (2015)
  33. Maleknejad, A., Sheikh-Jabbari, M.: Phys. Rev. D 84, 043515 (2011). arXiv:1102.1932 [hep-ph] ADSCrossRefGoogle Scholar
  34. Maleknejad, A., Sheikh-Jabbari, M.: Phys. Lett. B 723, 224 (2013). arXiv:1102.1513 [hep-ph] ADSMathSciNetCrossRefGoogle Scholar
  35. Maleknejad, A., Sheikh-Jabbari, M., Soda, J.: Phys. Rep. 528, 161 (2013). arXiv:1212.2921 [hep-th] ADSMathSciNetCrossRefGoogle Scholar
  36. Mangano, G., Miele, G., Pastor, S., Peloso, M.: Phys. Lett. B 534, 8 (2002). arXiv:astro-ph/0111408 [astro-ph] ADSCrossRefGoogle Scholar
  37. Martinec, E., Adshead, P., Wyman, M.: J. High Energy Phys. 02, 027 (2013). arXiv:1206.2889 [hep-th] ADSCrossRefGoogle Scholar
  38. Mehrabi, A., Basilakos, S., Malekjani, M., Davari, Z.: Phys. Rev. D 92, 123513 (2015a). arXiv:1510.03996 [astro-ph.CO] ADSCrossRefGoogle Scholar
  39. Mehrabi, A., Basilakos, S., Pace, F.: Mon. Not. R. Astron. Soc. 452, 2930 (2015b). arXiv:1504.01262 [astro-ph.CO]. doi: 10.1093/mnras/stv1478 ADSCrossRefGoogle Scholar
  40. Nobbenhuis, S.: The cosmological constant problem, an inspiration for new physics. Ph.D. Thesis, Utrecht University (2006). arXiv:gr-qc/0609011 [gr-qc]
  41. Padmanabhan, N., Xu, X., Eisenstein, D.J., Scalzo, R., Cuesta, A.J., et al.: Mon. Not. R. Astron. Soc. 427, 2132 (2012). arXiv:1202.0090 [astro-ph.CO] ADSCrossRefGoogle Scholar
  42. Peebles, P., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003). arXiv:astro-ph/0207347 [astro-ph] ADSCrossRefGoogle Scholar
  43. Percival, W.J., Cole, S., Eisenstein, D.J., Nichol, R.C., Peacock, J.A., Pope, A.C., Szalay, A.S.: Mon. Not. R. Astron. Soc. 381, 1053 (2007). arXiv:0705.3323 [astro-ph] ADSCrossRefGoogle Scholar
  44. Perlmutter, S., et al. (Supernova Cosmology Project): Astrophys. J. 517, 565 (1999). arXiv:astro-ph/9812133 [astro-ph] ADSCrossRefGoogle Scholar
  45. Riess, A.G., et al. (Supernova Search Team): Astron. J. 116, 1009 (1998). arXiv:astro-ph/9805201 [astro-ph] ADSCrossRefGoogle Scholar
  46. Riess, A.G., et al.: Astron. J. 117, 707 (1999). arXiv:astro-ph/9810291 [astro-ph] ADSCrossRefGoogle Scholar
  47. Rinaldi, M.: arXiv:1508.04576 [gr-qc] (2015)
  48. Sahni, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 9, 373 (2000). arXiv:astro-ph/9904398 [astro-ph] ADSGoogle Scholar
  49. Setare, M.R., Kamali, V.: Phys. Lett. B 726, 56 (2013). arXiv:1309.2452 [gr-qc] ADSCrossRefGoogle Scholar
  50. Setare, M.R., Kamali, V.: Gen. Relativ. Gravit. 46, 1642 (2014). arXiv:1308.5674 [gr-qc] ADSCrossRefGoogle Scholar
  51. Sheikh-Jabbari, M.: Phys. Lett. B 717, 6 (2012). arXiv:1203.2265 [hep-th] ADSCrossRefGoogle Scholar
  52. Song, Y.-S., Taruya, A., Linder, E., Koyama, K., Sabiu, C.G., Zhao, G.-B., Bernardeau, F., Nishimichi, T., Okumura, T.: Phys. Rev. D 92, 043522 (2015). arXiv:1507.01592 [astro-ph.CO] ADSCrossRefGoogle Scholar
  53. Spergel, D., et al. (WMAP Collaboration): Astrophys. J. Suppl. 148, 175 (2003). arXiv:astro-ph/0302209 [astro-ph] ADSCrossRefGoogle Scholar
  54. Suzuki, N., et al.: Astrophys. J. 746, 85 (2012a). arXiv:1105.3470 [astro-ph.CO] ADSCrossRefGoogle Scholar
  55. Suzuki, N., Rubin, D., Lidman, C., Aldering, G., et al.: Astrophys. J. 746, 85 (2012b). arXiv:1105.3470 [astro-ph] ADSCrossRefGoogle Scholar
  56. Tegmark, M., et al. (SDSS Collaboration): Phys. Rev. D 69, 103501 (2004). arXiv:astro-ph/0310723 [astro-ph] ADSCrossRefGoogle Scholar
  57. Tegmark, M., et al. (SDSS Collaboration): Phys. Rev. D 74, 123507 (2006). arXiv:astro-ph/0608632 [astro-ph] ADSCrossRefGoogle Scholar
  58. Tsujikawa, S.: Lect. Notes Phys. 800, 99 (2010). arXiv:1101.0191 [gr-qc] ADSCrossRefGoogle Scholar
  59. Tsujikawa, S.: Dark energy: investigation and modeling. In: Dark Matter and Dark Energy. Astrophysics and Space Science Library, vol. 307, p. 331. Springer, Berlin (2011). arXiv:1004.1493 [astro-ph.CO] CrossRefGoogle Scholar
  60. Tsujikawa, S.: Class. Quantum Gravity 30, 214003 (2013). arXiv:1304.1961 [gr-qc] ADSCrossRefGoogle Scholar
  61. Weinberg, S.: Rev. Mod. Phys. 61, 1 (1989) ADSCrossRefGoogle Scholar
  62. Wu, W.L.K., Errard, J., Dvorkin, C., Kuo, C.L., Lee, A.T., McDonald, P., Slosar, A., Zahn, O.: Astrophys. J. 788, 138 (2014). arXiv:1402.4108 [astro-ph.CO] ADSCrossRefGoogle Scholar
  63. Zhang, H., Li, C.S., Cao, Q.-H., Li, Z.: Phys. Rev. D 82, 075003 (2010). arXiv:0910.2831 [hep-ph] ADSCrossRefGoogle Scholar
  64. Zlatev, I., Wang, L.-M., Steinhardt, P.J.: Phys. Rev. Lett. 82, 896 (1999). arXiv:astro-ph/9807002 [astro-ph] ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of PhysicsBu-Ali Sina UniversityHamedanIran
  2. 2.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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