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Astrophysics and Space Science

, 363:230 | Cite as

An interacting new holographic dark energy in the framework of fractal cosmology

  • Ehsan Sadri
  • Martiros Khurshudyan
  • Surajit Chattopadhyay
Original Article
  • 71 Downloads

Abstract

In this paper, we study an interacting holographic dark energy model in the framework of fractal cosmology. The features of fractal cosmology could pass ultraviolet divergencies and also make a better understanding of the universe in different dimensions. We discuss a fractal FRW universe filled with the dark energy and cold dark matter interacting with each other. It is observed that the Hubble parameter embraces the recent observational range while the deceleration parameter demonstrates an accelerating universe and a behavior similar to \(\Lambda \mbox{CDM}\). Plotting the equation of state shows that it lies in phantom region for interaction mode. We use \(\mathit{Om}\)-diagnostic tool and it shows a phantom behavior of dark energy which is a condition of avoiding the formation of black holes. Finally we execute the StateFinder diagnostic pair and all the trajectories for interacting and non-interacting state of the model meet the fixed point \(\Lambda \mbox{CDM}\) at the start of the evolution. A behavior similar to Chaplygin gas also can be observed in statefinder plane. We find that new holographic dark energy model (NHDE) in fractal cosmology expressed the consistent behavior with recent observational data and can be considered as a model to avoid the formation of black holes in comparison with the main model of NHDE in the simple FRW universe. It has also been observed that for the interaction term varying with matter density, the model generates asymptotic de-Sitter solution. However, if the interaction term varies with energy density, then the model shows Big-Rip singularity. Using our modified CAMB code, we observed that the interacting model suppresses the CMB spectrum at low multipoles \(l<50\) and enhances the acoustic peaks. Based on the observational data sets used in this paper and using Metropolis-Hastings method of MCMC numerical calculation, it seems that the best value with \(1\sigma \) and \(2\sigma \) confidence interval are \(\Omega _{m0}=0.278^{+0.008~+0.010} _{-0.007~-0.009}\), \(H_{0}=69.9^{+0.95~+1.57}_{-0.95~-1.57}\), \(r_{c}=0.08^{+0.02~+0.027}_{-0.002~-0.0027}\), \(\beta =0.496^{+0.005~+0.009} _{-0.005~-0.009}\), \(c= 0.691^{+0.024~+0.039}_{-0.025~-0.037}\) and \(b^{2}=0.035\) according to which we find that the proposed model in the presence of interaction is compatible with the recent observational data.

Keywords

Holographic dark energy Fractal cosmology Phantom dark energy The coupling constant Black hole 

Notes

Acknowledgements

We would like to thank the referee for insightful comments which improved the quality of the paper. Martiros Khurshudyan is supported in part by Chinese Academy of Sciences President’s International Fellowship Initiative Grant (No. 2018PM0054). Surajit Chattopadhyay is financially supported by CSIR Grant 03(1420)/18/EMR-II.

Compliance with ethical standards

The authors hereby ensure that the accepted principles of ethical and professional conduct have been followed.

References

  1. Ade, P.A., Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J., Baccigalupi, C., Banday, A., Barreiro, R., Bartlett, J., Bartolo, N., et al.: Astron. Astrophys. 594, A13 (2016) Google Scholar
  2. Aghanim, N., Akrami, Y., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A., Barreiro, R., Bartolo, N., Basak, S., et al.: Planck 2018 results. VI. Cosmological parameters (2018). arXiv preprint arXiv:1807.06209
  3. Aida, T.: Nucl. Phys. 444, 353 (1995) ADSGoogle Scholar
  4. Akbar, M., Cai, R.-G.: Phys. Lett. B 648, 243 (2007) ADSMathSciNetGoogle Scholar
  5. Alam, U., Sahni, V., Deep Saini, T., Starobinsky, A.: Mon. Not. R. Astron. Soc. 344(4), 1057–1074 (2003) ADSGoogle Scholar
  6. Amarilla, L., Eiroa, E.F.: Phys. Rev. D 85, 064019 (2012) ADSGoogle Scholar
  7. Amendola, L.: Phys. Rev. D 60(4), 043501 (1999) ADSGoogle Scholar
  8. Astashenok, A.V., Nojiri, S., Odintsov, S.D., Yurov, A.V.: Phys. Lett. B 709, 396 (2012) ADSGoogle Scholar
  9. Bamba, K., et al.: Eur. Phys. J. C 67, 295 (2010) ADSGoogle Scholar
  10. Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.: Astrophys. Space Sci. 342, 155 (2012) ADSGoogle Scholar
  11. Banerjee, N., Pavon, D.: Phys. Lett. B 647(5), 477–481 (2007) ADSMathSciNetGoogle Scholar
  12. Betoule, M., et al.: Astron. Astrophys. 568, A22 (2014) Google Scholar
  13. Bolotin, Y.L., Kostenko, A., Lemets, O.A., Yerokhin, D.A.: Int. J. Mod. Phys. D 24, 1530007 (2015) ADSGoogle Scholar
  14. Bousso, R.: Rev. Mod. Phys. 74, 825 (2002) ADSGoogle Scholar
  15. Cai, Y., Saridakis, E.N., Setare, M., Xia, J.Q.: Phys. Rep. 493(1), 1–60 (2010) ADSMathSciNetGoogle Scholar
  16. Calcagni, G.: Phys. Rev. Lett. 104(25), 251301 (2010a) ADSGoogle Scholar
  17. Calcagni, G.: J. High Energy Phys. 2010(3), 1 (2010b) Google Scholar
  18. Caldera-Cabral, G., Maartens, R., Urena-Lopez, L.A.: Phys. Rev. D 79(6), 063518 (2009) ADSGoogle Scholar
  19. Caldwell, R.R., Kamionkowski, M.: Annu. Rev. Astron. Astrophys. 59, 397 (2009) Google Scholar
  20. Cao, S.-L., Teng, H.-Y., Wan, H.-Y., Yu, H.-R., Zhang, T.-J.: Eur. Phys. J. C 78, 170 (2018) ADSGoogle Scholar
  21. Cheng-Yi, S.: Commun. Theor. Phys. 52(3), 441 (2009) ADSMathSciNetGoogle Scholar
  22. Christensen, S., Duff, M.J.: Phys. Lett. B 79, 213 (1978) ADSGoogle Scholar
  23. Cohen, A., Kaplan, D., Nelson, A.: Phys. Rev. Lett. 82, 4971 (1999) ADSMathSciNetGoogle Scholar
  24. Conde-Saavedra, G., Iribarrem, A., Ribeiro, M.B.: Physica A, 417, 332 (2015) ADSGoogle Scholar
  25. Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006) ADSGoogle Scholar
  26. Dabrowski, M.P., Denkiewicz, T.: Phys. Rev. D 79, 063521 (2009) ADSMathSciNetGoogle Scholar
  27. Deffayet, C.: Phys. Lett. B 502, 199 (2001) ADSGoogle Scholar
  28. Deffayet, C., Dvali, G., Gabadadze, G.: Phys. Rev. D 65, 044023 (2002) ADSMathSciNetGoogle Scholar
  29. Del Campo, S., Fabris, J.C., Herrera, R., Zimdahl, W.: Phys. Rev. D 83(12), 123006 (2011) ADSGoogle Scholar
  30. Dvali, G., Gabadadze, G., Porrati, M.: Phys. Lett. B 485, 208 (2000) ADSMathSciNetGoogle Scholar
  31. Feng, C., et al.: Phys. Lett. B 665(2), 111–119 (2008) ADSGoogle Scholar
  32. Frieman, J.A., Turner, M.S., Huterer, D.: Annu. Rev. Astron. Astrophys. 46, 385 (2008) ADSGoogle Scholar
  33. Gallavotti, G.: Rev. Mod. Phys. 57, 471 (1985) ADSGoogle Scholar
  34. Gastmans, R., Kallosh, R., Truffin, C.: Nucl. Phys. B 133, 417 (1978) ADSGoogle Scholar
  35. Gong, Y.: Phys. Rev. D 70(6), 064029 (2004) ADSGoogle Scholar
  36. Gonzalez, J., Guzman, F.: Phys. Rev. D 79, 121501 (2009) ADSGoogle Scholar
  37. Guo, Z., Ohta, N., Tsujikawa, S.: Phys. Rev. D 76(2), 023508 (2007) ADSGoogle Scholar
  38. Hao, W.: Commun. Theor. Phys. 52(4), 743 (2009) Google Scholar
  39. Hilfer, R.: Applications of Fractional Calculus in Physics (2000) zbMATHGoogle Scholar
  40. Hooft, G.: arXiv preprint gr-qc/9310026 (1993)
  41. Hsu, S.D.: Phys. Lett. B 594, 13 (2004) ADSGoogle Scholar
  42. Hu, W., Sugiyama, N.: Astron. J. 471, 542 (1996) ADSGoogle Scholar
  43. Huang, Q.G., Li, M.: J. Cosmol. Astropart. Phys. 2004(08), 013 (2004) Google Scholar
  44. Ito, M.: Europhys. Lett. 71(5), 712 (2005) ADSGoogle Scholar
  45. Jacobson, T.: Phys. Rev. Lett. 75, 1260 (1995) ADSMathSciNetGoogle Scholar
  46. Jamil, M., Saridakis, E.N., Setare, M.: Phys. Lett. B 679(3), 172–176 (2009) ADSGoogle Scholar
  47. Jawad, A.: Astrophys. Space Sci. 353(2), 691 (2014) ADSGoogle Scholar
  48. Jawad, A., Majeed, A.: Astrophys. Space Sci. 356(2), 375 (2015) ADSGoogle Scholar
  49. Jawad, A., Rani, S., Salako, I.G., Gulshan, F.: Int. J. Mod. Phys. D 26, 1750049 (2017) ADSGoogle Scholar
  50. Karami, K., Jamil, M., Ghaffari, S., Fahimi, K., Myrzakulov, R.: Can. J. Phys. 91, 770 (2013) ADSGoogle Scholar
  51. Khurshudyan, M.: Astrophys. Space Sci. 361, 232 (2016a) ADSGoogle Scholar
  52. Khurshudyan, M.: Symmetry, vol. 8, p. 110 (2016b) Google Scholar
  53. Kim, H., Lee, H.W., Myung, Y.S.: Phys. Lett. B 632(5), 605–609 (2006) ADSGoogle Scholar
  54. Knizhnik, V., Zamolodchikov, A.: Nucl. Phys. B 690 (1984) Google Scholar
  55. Kothawala, D., Sarkar, S., Padmanabhan, T.: Phys. Lett. B 652, 338 (2007) ADSMathSciNetGoogle Scholar
  56. Krasinski, A.: Inhomogeneous cosmological models (1997 and 2006) Google Scholar
  57. Labini, F.S.: Astron. Astrophys. Trans. 19, 397 (2000) ADSGoogle Scholar
  58. Labini, F.S.: Europhys. Lett. 96, 59001 (2011) ADSGoogle Scholar
  59. Lemets, O., Yerokhin, D.: arXiv preprint arXiv:1202.3457 (2012)
  60. Lewis, A., Challinor, A., Lasenby, A.: Astrophys. J. 538, 473 (2000) ADSGoogle Scholar
  61. Lewis, A., Challinor, A., Lasenby, A.: AMB: code for anisotropies in the microwave background. In: ASCL (2011) Google Scholar
  62. Li, M.: Phys. Lett. B 603(1), 1–5 (2004a) ADSMathSciNetGoogle Scholar
  63. Li, M.: Phys. Lett. B 603, 1 (2004b) ADSMathSciNetGoogle Scholar
  64. Li, M., Li, X., Wang, S., Wand, Y.: Commun. Theor. Phys. 56, 525 (2011) ADSGoogle Scholar
  65. Li, M., Li, X.-D., Wang, S., Wang, Y.: Front. Phys., 8, 828 (2013a) Google Scholar
  66. Li, Y.-H., Wang, S., Li, X.-D., Zhang, X.: J. Cosmol. Astropart. Phys. 2013, 033 (2013b) Google Scholar
  67. Linde, A.D.: Phys. Lett. B 175, 395 (1986) ADSGoogle Scholar
  68. Maartens, R., Koyama, K.: Living Rev. Relativ. 13, 5 (2010) ADSGoogle Scholar
  69. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 103522, 70 (2004) Google Scholar
  70. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 72, 023003 (2005) ADSGoogle Scholar
  71. Nojiri, S., Odintsov, S.D.: Gen. Relativ. Gravit. 38, 1285 (2006) ADSGoogle Scholar
  72. Nojiri, S., Odintsov, S.: Eur. Phys. J. C 77, 528 (2017) ADSGoogle Scholar
  73. Nojiri, S., Odintsov, S.D., Sasaki, M.: Phys. Rev. D 71, 123509 (2005a) ADSGoogle Scholar
  74. Nojiri, S., Odintsov, S.D., Tsujikawa, S.: Phys. Rev. D 71, 063004 (2005b) ADSGoogle Scholar
  75. Padmanabhan, T.: Phys. Rep. 380, 235 (2003) ADSMathSciNetGoogle Scholar
  76. Padmanabhan, T., Paranjape, A.: Phys. Rev. D 75, 064004 (2007) ADSMathSciNetGoogle Scholar
  77. Paranjape, A., Sarkar, S., Padmanabhan, T.: Phys. Rev. D 74, 104015 (2006) ADSMathSciNetGoogle Scholar
  78. Pavón, D., Wang, B.: Gen. Relativ. Gravit. 41(1), 1–5 (2009) ADSGoogle Scholar
  79. Pavón, D., Zimdahl, W.: Phys. Lett. B 628(3), 206–210 (2005) ADSGoogle Scholar
  80. Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003) ADSGoogle Scholar
  81. Perlmutter, S., et al.: Astron. J. 517(2), 565 (1999) Google Scholar
  82. Ribeiro, M.B., Miguelote, A.Y.: Braz. J. Phys. 28, 132 (1998) ADSGoogle Scholar
  83. Riess, G., et al.: Astron. J. 116(3), 1009 (1998) ADSGoogle Scholar
  84. Sadri, E., Vakili, B.: Astrophys. Space Sci. 363, 13 (2018) ADSGoogle Scholar
  85. Sahni, V., Saini, T.D., Starobinsky, A.A., Alam, U.: JETP Lett. 77(5), 201–206 (2003) ADSGoogle Scholar
  86. Sahni, V., Shafieloo, A., Starobinsky, A.A.: Phys. Rev. D 78(10), 103502 (2008) ADSGoogle Scholar
  87. Salti, M., Korunur, M., Acikgoz, I.: Eur. Phys. J. Plus 129, 95 (2014) Google Scholar
  88. Setare, M.: Phys. Lett. B 642(1), 1–4 (2006) ADSMathSciNetGoogle Scholar
  89. Setare, M.: J. Cosmol. Astropart. Phys. 2007(01), 023 (2007a) Google Scholar
  90. Setare, M.: Phys. Lett. B 644(2), 99–103 (2007b) ADSMathSciNetGoogle Scholar
  91. Setare, M., Saridakis, E.: Phys. Lett. B 671(3), 331–338 (2009a) ADSGoogle Scholar
  92. Setare, M., Saridakis, E.: J. Cosmol. Astropart. Phys. 2009(03), 002 (2009b) Google Scholar
  93. Alam, S., et al.: Mon. Not. R. Astron. Soc. 470, 2617–2652 (2017) ADSGoogle Scholar
  94. Sheykhi, A.: J. Cosmol. Astropart. Phys. 2009(05), 019 (2009) Google Scholar
  95. Sheykhi, A., Wang, B.: Mod. Phys. Lett. A 25, 1199 (2010) ADSGoogle Scholar
  96. Sheykhi, A., Wang, B., Cai, R.G.: Phys. Rev. D 76(2), 023515 (2007a) ADSMathSciNetGoogle Scholar
  97. Sheykhi, A., Wang, B., Cai, R.G.: Nucl. Phys. B 779(1), 1–12 (2007b) ADSGoogle Scholar
  98. Sheykhi, A., Dehghani, M., Hosseini, S.: Phys. Lett. B 726, 23 (2013a) ADSGoogle Scholar
  99. Sheykhi, A., Teimoori, Z., Wang, B.: Phys. Lett. B 718, 1203 (2013b) ADSGoogle Scholar
  100. Sheykhi, A., Dehghani, M., Ghaffari, S.: Int. J. Mod. Phys. D 25(02), 1650018 (2016) ADSGoogle Scholar
  101. Susskind, L.: J. Math. Phys. 36(11), 6377–6396 (1995) ADSMathSciNetGoogle Scholar
  102. The LIGO Scientific Collaboration, The Virgo Collaboration, The 1M2H Collaboration, The Dark Energy Camera GW-EM Collaboration, The DES Collaboration, The DLT40 Collaboration, The Las Cumbres Observatory Collaboration, The VINROUGE Collaboration, The MASTER Collaboration: Nature 551, 85 (2017) Google Scholar
  103. Thomas, S.: Phys. Rev. Lett. 89, 081301 (2002) ADSMathSciNetGoogle Scholar
  104. Wang, Y., Mukherjee, P.: Astrophys. J., 76, 103533 (2007) Google Scholar
  105. Wang, B., Gong, Y., Abdalla, E.: Phys. Lett. B 624(3), 141–146 (2005) ADSGoogle Scholar
  106. Wang, B., Abdalla, E., Atrio-Barandela, F., Pavon, D.: Rep. Prog. Phys. 79(5), 096901 (2016a) ADSGoogle Scholar
  107. Wang, S., Wang, Y., Li, M.: arXiv preprint arXiv:1612.00345 (2016b)
  108. Wei, H.: Class. Quantum Gravity 29, 175008 (2012) ADSGoogle Scholar
  109. Wei, H., Zhang, S.N.: Phys. Rev. D 76(6), 063003 (2007) ADSGoogle Scholar
  110. Weinberg, S.: Ultraviolet Divergences in Quantum Theories of Gravitation (1979) Google Scholar
  111. Zhang, X.: Int. J. Mod. Phys. D 14(09), 1597–1606 (2005) ADSGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Ehsan Sadri
    • 1
  • Martiros Khurshudyan
    • 2
    • 3
    • 4
    • 5
  • Surajit Chattopadhyay
    • 6
  1. 1.Department of Physics, Central Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.International Laboratory for Theoretical CosmologyTomsk State University of Control Systems and RadioelectronicsTomskRussia
  3. 3.Research DivisionTomsk State Pedagogical UniversityTomskRussia
  4. 4.CAS Key Laboratory for Research in Galaxies and Cosmology, Department of AstronomyUniversity of Science and Technology of ChinaHefeiP.R. China
  5. 5.School of Astronomy and Space Science University of Science and Technology of ChinaHefeiP.R. China
  6. 6.Department of MathematicsAmity UniversityNew TownIndia

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