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Diagnosing holographic type dark energy models with the Statefinder hierarchy, composite null diagnostic and w-w′ pair

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Abstract

The main purpose of this work is to distinguish various holographic type dark energy (DE) models, including the ΛHDE, HDE, NADE, and RDE model, by using various diagnostic tools. The first diagnostic tool is the Statefinder hierarchy, in which the evolution of Statefinder hierarchy parmeter S (1) 3(z) and S (1) 4(z) are studied. The second is composite null diagnostic (CND), in which the trajectories of {S (1) 3, ϵ} and {S (1) 4, ϵ} are investigated, where ϵ is the fractional growth parameter. The last is w-w′ analysis, where w is the equation of state for DE and the prime denotes derivative with respect to lna. In the analysis we consider two cases: varying current fractional DE density Ω de0 and varying DE model parameter C. We find that: (1) both the Statefinder hierarchy and the CND have qualitative impact on ΛHDE, but only have quantitative impact on HDE. (2) S (1) 4 can lead to larger differences than S (1) 3, while the CND pair has a stronger ability to distinguish different models than the Statefinder hierarchy. (3) For the case of varying C, the {w,w′} pair has qualitative impact on ΛHDE; for the case of varying Ω de0, the {w, w′} pair only has quantitative impact; these results are different from the cases of HDE, RDE, and NADE, in which the {w,w′} pair only has quantitative impact on these models. In conclusion, compared with HDE, RDE, and NADE, the ΛHDE model can be easily distinguished by using these diagnostic tools.

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References

  1. A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff, and J. Tonry, Astron. J. 116, 1009 (1998).

    Article  ADS  Google Scholar 

  2. S. Perlmutter, et al. (Supernova Cosmology Project Collaboration), Astrophys. J. 517, 565 (1999).

    ADS  Google Scholar 

  3. D. N. Spergel, et al. (WMAP Collaboration), Astrophys. J. Suppl. S. 148, 175 (2003).

    Article  ADS  Google Scholar 

  4. D. N. Spergel, R. Bean, O. Dore, M. R. Nolta, C. L. Bennett, J. Dunkley, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, Astrophys. J. Suppl. S. 170, 377 (2007).

    Article  ADS  Google Scholar 

  5. Planck Collaboration, Astron. Astrophys. 571, A16 (2014).

  6. Planck Collaboration, Astron. Astrophys. 594, A13 (2016).

  7. D. J. Eisenstein, I. Zehavi, D. W. Hogg, R. Scoccimarro, M. R. Blanton, R. C. Nichol, R. Scranton, H. J. Seo, M. Tegmark, Z. Zheng, S. F. Anderson, J. Annis, N. Bahcall, J. Brinkmann, S. Burles, F. J. Castander, A. Connolly, I. Csabai, M. Doi, M. Fukugita, J. A. Frieman, K. Glazebrook, J. E. Gunn, J. S. Hendry, G. Hennessy, Z. Ivezi´c, S. Kent, G. R. Knapp, H. Lin, Y. S. Loh, R. H. Lupton, B. Margon, T. A. McKay, A. Meiksin, J. A. Munn, A. Pope, M. W. Richmond, D. Schlegel, D. P. Schneider, K. Shimasaku, C. Stoughton, M. A. Strauss, M. SubbaRao, A. S. Szalay, I. Szapudi, D. L. Tucker, B. Yanny, and D. G. York, Astrophys. J. 633, 560 (2005).

    Article  ADS  Google Scholar 

  8. W. J. Percival, B. A. Reid, D. J. Eisenstein, N. A. Bahcall, T. Budavari, J. A. Frieman, M. Fukugita, J. E. Gunn, Ivezi´c, G. R. Knapp, R. G. Kron, J. Loveday, R. H. Lupton, T. A. McKay, A. Meiksin, R. C. Nichol, A. C. Pope, D. J. Schlegel, D. P. Schneider, D. N. Spergel, C. Stoughton, M. A. Strauss, A. S. Szalay, M. Tegmark, M. S. Vogeley, D. H. Weinberg, D. G. York, and I. Zehavi, Mon. Not. R. Astron. Soc. 401, 2148 (2010).

    Article  ADS  Google Scholar 

  9. E. J. Copeland, M. Sami, and S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006).

    Article  ADS  Google Scholar 

  10. J. A. Frieman, M. S. Turner, and D. Huterer, Annu. Rev. Astron. Astrophys. 46, 385 (2008).

    Article  ADS  Google Scholar 

  11. M. Li, X. D. Li, S. Wang, and Y. Wang, Commun. Theor. Phys. 56, 525 (2011).

    Article  ADS  Google Scholar 

  12. M. Li, X. D. Li, S. Wang, and Y. Wang, Front. Phys. 8, 828 (2013).

    Article  Google Scholar 

  13. I. Zlatev, L.Wang, and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999).

    Article  ADS  Google Scholar 

  14. C. Armendáriz-Pićon, T. Damour, and V. Mukhanov, Phys. Lett. B 458, 209 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  15. A. Kamenshchik, U. Moschella, and V. Pasquier, Phys. Lett. B 511, 265 (2001).

    Article  ADS  Google Scholar 

  16. R. R. Caldwell, Phys. Lett. B 545, 23 (2002).

    Article  ADS  Google Scholar 

  17. T. Padmanabhan, Phys. Rev. D 66, 021301 (2002).

    Article  ADS  Google Scholar 

  18. R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).

    Article  ADS  Google Scholar 

  19. B. Feng, X. Wang, and X. Zhang, Phys. Lett. B 607, 35 (2005).

    Article  ADS  Google Scholar 

  20. H. Wei, R. G. Cai, and D. F. Zeng, Class. Quant. Grav. 22, 3189 (2005).

    Article  ADS  Google Scholar 

  21. T. Y. Xia, and Y. Zhang, Phys. Lett. B 656, 19 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  22. S. Wang, Y. Zhang, and T. Y. Xia, J. Cosmol. Astropart. Phys. 2008, 037 (2008).

    Article  Google Scholar 

  23. S. Wang, and Y. Zhang, Phys. Lett. B 669, 201 (2008).

    Article  ADS  Google Scholar 

  24. G.’ t Hooft, arXiv: gr-qc/9310026.

  25. L. Susskind, J. Math. Phys. 36, 6377 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  26. M. Li, Phys. Lett. B 603, 1 (2004)

  27. Q. G. Huang, and Y. Gong, J. Cosmol. Astropart. Phys. 2004, 006 (2004).

    Article  Google Scholar 

  28. X. Zhang, and F. Q. Wu, Phys. Rev. D 72, 043524 (2005).

    Article  ADS  Google Scholar 

  29. M. Li, X. D. Li, S. Wang, and X. Zhang, J. Cosmol. Astropart. Phys. 2009, 036 (2009).

    Article  Google Scholar 

  30. M. Li, X. D. Li, S. Wang, Y. Wang, and X. Zhang, J. Cosmol. Astropart. Phys. 2009, 014 (2009).

    Article  Google Scholar 

  31. Q. G. Huang, M. Li, X. D. Li, and S. Wang, Phys. Rev. D 80, 083515 (2009).

    Article  ADS  Google Scholar 

  32. S. Wang, X. D. Li, and M. Li, Phys. Rev. D 82, 103006 (2010).

    Article  ADS  Google Scholar 

  33. X. D. Li, S. Li, S. Wang, W. S. Zhang, Q. G. Huang, and M. Li, J. Cosmol. Astropart. Phys. 2011, 011 (2011).

    Article  Google Scholar 

  34. Q. G. Huang, and M. Li, J. Cosmol. Astropart. Phys. 2004, 013 (2004).

    Article  Google Scholar 

  35. B. Wang, Y. Gong, and E. Abdalla, Phys. Lett. B 624, 141 (2005).

    Article  ADS  Google Scholar 

  36. D. Pav´on, and W. Zimdahl, Phys. Lett. B 628, 206 (2005).

    Article  ADS  Google Scholar 

  37. S. Nojiri, and S. D. Odintsov, Gen. Relativ. Gravit. 38, 1285 (2006).

    Article  ADS  Google Scholar 

  38. X. D. Li, S.Wang, Q. G. Huang, X. Zhang, and M. Li, Sci. China-Phys. Mech. Astron. 55, 1330 (2012).

    Article  ADS  Google Scholar 

  39. J. L. Cui, Y. Y. Xu, J. F. Zhang, and X. Zhang, Sci. China-Phys. Mech. Astron. 58, 110402 (2015).

    Article  Google Scholar 

  40. D. Z. He, J. F. Zhang, and X. Zhang, Sci. China-Phys. Mech. Astron. 60, 039511 (2017).

    Article  ADS  Google Scholar 

  41. S. Wang, Y. Z. Hu, and M. Li, Sci. China-Phys. Mech. Astron. 60, 040411 (2017).

    Article  ADS  Google Scholar 

  42. H. Wei, and R. G. Cai, Phys. Lett. B 660, 113 (2008).

    Article  ADS  Google Scholar 

  43. C. Gao, F. Wu, X. Chen, and Y. G. Shen, Phys. Rev. D 79, 043511 (2009).

    Article  ADS  Google Scholar 

  44. S. Wang, Y. Wang, and M. Li, Phys. Rep. 696, 1 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  45. G. Bertone, D. Hooper, and J. Silk, Phys. Rep. 405, 279 (2005).

    Article  ADS  Google Scholar 

  46. Y. Hu, M. Li, N. Li, and Z. Zhang, J. Cosmol. Astropart. Phys. 2015, 012 (2015).

    Article  Google Scholar 

  47. S. Wang, S. Wen, L. Zhou, and M. Li, Mon. Not. R. Astron. Soc. 467, 961 (2017).

    ADS  Google Scholar 

  48. M. Arabsalmani, and V. Sahni, Phys. Rev. D 83, 043501 (2011).

    Article  ADS  Google Scholar 

  49. V. Sahni, T. D. Saini, A. A. Starobinsky, and U. Alam, J. Exp. Theor. Phys. Lett. 77, 201 (2003).

    Article  Google Scholar 

  50. U. Alam, V. Sahni, T. Deep Saini, and A. A. Starobinsky, Mon. Not. Roy. Astron. Soc. 344, 1057 (2003).

    Article  ADS  Google Scholar 

  51. R. R. Caldwell, and E. V. Linder, Phys. Rev. Lett. 95, 141301 (2005).

    Article  ADS  Google Scholar 

  52. R. Myrzakulov, and M. Shahalam, J. Cosmol. Astropart. Phys. 2013, 047 (2013).

    Article  Google Scholar 

  53. F. Yu, J. L. Cui, J. F. Zhang, and X. Zhang, Eur. Phys. J. C 75, 274 (2015).

    Article  ADS  Google Scholar 

  54. J. F. Zhang, J. L. Cui, and X. Zhang, Eur. Phys. J. C 74, 3100 (2014).

    Article  Google Scholar 

  55. L. J. Zhou, and S. Wang, Sci. China-Phys. Mech. Astron. 59, 670411 (2016).

    Article  Google Scholar 

  56. T. Chiba, and T. Nakamura, Prog. Theor. Phys. 100, 1077 (1998).

    Article  ADS  Google Scholar 

  57. V. Acquaviva, A. Hajian, D. N. Spergel, and S. Das, Phys. Rev. D 78, 043514 (2008).

    Article  ADS  Google Scholar 

  58. L. Wang, and P. J. Steinhardt, Astrophys. J. 508, 483 (1998).

    Article  ADS  Google Scholar 

  59. A. Pavlov, O. Farooq, and B. Ratra, Phys. Rev. D 90, 023006 (2014).

    Article  ADS  Google Scholar 

  60. Y. H. Li, S. Wang, X. D. Li, and X. Zhang, J. Cosmol. Astropart. Phys. 2013, 033 (2013).

    Article  Google Scholar 

  61. H. Wei, and R. G. Cai, Phys. Lett. B 663, 1 (2008).

    Article  ADS  Google Scholar 

  62. J. F. Zhang, Y. H. Li, and X. Zhang, Eur. Phys. J. C 73, 2280 (2013).

    Article  ADS  Google Scholar 

  63. X. Zhang, Phys. Rev. D 79, 103509 (2009).

    Article  ADS  Google Scholar 

  64. S. Wang, and Y. Wang, Phys. Rev. D 88, 043511 (2013).

    Article  ADS  Google Scholar 

  65. Y. Wang, and S. Wang, Phys. Rev. D 88, 043522 (2013).

    Article  ADS  Google Scholar 

  66. S. Wang, Y. H. Li, and X. Zhang, Phys. Rev. D 89, 063524 (2014).

    Article  ADS  Google Scholar 

  67. S. Wang, Y. Z. Wang, J. J. Geng, and X. Zhang, Eur. Phys. J. C 74, 3148 (2014).

    Article  ADS  Google Scholar 

  68. S. Wang, Y. Z. Wang, and X. Zhang, Commun. Theor. Phys. 62, 927 (2014).

    Article  ADS  Google Scholar 

  69. S. Wang, J. J. Geng, Y. L. Hu, and X. Zhang, Sci. China-Phys. Mech. Astron. 58, 019801 (2015).

    Google Scholar 

  70. S. Wang, Y. Hu, M. Li, and N. Li, Astrophys. J. 821, 60 (2016).

    Article  ADS  Google Scholar 

  71. M. Li, N. Li, S. Wang, and L. Zhou, Mon. Not. R. Astron. Soc. 460, 2586 (2016).

    Article  ADS  Google Scholar 

  72. Y. Hu, M. Li, N. Li, and S. Wang, Astron. Astrophys. 592, A101 (2016).

    Article  ADS  Google Scholar 

  73. S. Wang, S. Wen, and M. Li, J. Cosmol. Astropart. Phys. 2017, 037 (2017).

    Article  Google Scholar 

  74. S. X. Wen, and S. Wang, arXiv: 1708.03143.

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Authors and Affiliations

  1. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Ze Zhao

  2. School of Physical Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Ze Zhao

  3. School of Astronomy and Space Science, Sun Yat-Sen University, Guangzhou, 510275, China

    Shuang Wang

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  1. Ze Zhao
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  2. Shuang Wang
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Correspondence to Shuang Wang.

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Zhao, Z., Wang, S. Diagnosing holographic type dark energy models with the Statefinder hierarchy, composite null diagnostic and w-w′ pair. Sci. China Phys. Mech. Astron. 61, 039811 (2018). https://doi.org/10.1007/s11433-017-9111-4

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