Advertisement

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
  • 29 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) CrossRefGoogle 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) ADSCrossRefGoogle Scholar
  4. Akbar, M., Cai, R.-G.: Phys. Lett. B 648, 243 (2007) ADSMathSciNetCrossRefGoogle Scholar
  5. Alam, U., Sahni, V., Deep Saini, T., Starobinsky, A.: Mon. Not. R. Astron. Soc. 344(4), 1057–1074 (2003) ADSCrossRefGoogle Scholar
  6. Amarilla, L., Eiroa, E.F.: Phys. Rev. D 85, 064019 (2012) ADSCrossRefGoogle Scholar
  7. Amendola, L.: Phys. Rev. D 60(4), 043501 (1999) ADSCrossRefGoogle Scholar
  8. Astashenok, A.V., Nojiri, S., Odintsov, S.D., Yurov, A.V.: Phys. Lett. B 709, 396 (2012) ADSCrossRefGoogle Scholar
  9. Bamba, K., et al.: Eur. Phys. J. C 67, 295 (2010) ADSCrossRefGoogle Scholar
  10. Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.: Astrophys. Space Sci. 342, 155 (2012) ADSCrossRefGoogle Scholar
  11. Banerjee, N., Pavon, D.: Phys. Lett. B 647(5), 477–481 (2007) ADSMathSciNetCrossRefGoogle Scholar
  12. Betoule, M., et al.: Astron. Astrophys. 568, A22 (2014) CrossRefGoogle Scholar
  13. Bolotin, Y.L., Kostenko, A., Lemets, O.A., Yerokhin, D.A.: Int. J. Mod. Phys. D 24, 1530007 (2015) ADSCrossRefGoogle Scholar
  14. Bousso, R.: Rev. Mod. Phys. 74, 825 (2002) ADSMathSciNetCrossRefGoogle Scholar
  15. Cai, Y., Saridakis, E.N., Setare, M., Xia, J.Q.: Phys. Rep. 493(1), 1–60 (2010) ADSMathSciNetCrossRefGoogle Scholar
  16. Calcagni, G.: Phys. Rev. Lett. 104(25), 251301 (2010a) ADSCrossRefGoogle Scholar
  17. Calcagni, G.: J. High Energy Phys. 2010(3), 1 (2010b) CrossRefGoogle Scholar
  18. Caldera-Cabral, G., Maartens, R., Urena-Lopez, L.A.: Phys. Rev. D 79(6), 063518 (2009) ADSCrossRefGoogle 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) ADSCrossRefGoogle Scholar
  21. Cheng-Yi, S.: Commun. Theor. Phys. 52(3), 441 (2009) ADSMathSciNetCrossRefGoogle Scholar
  22. Christensen, S., Duff, M.J.: Phys. Lett. B 79, 213 (1978) ADSCrossRefGoogle Scholar
  23. Cohen, A., Kaplan, D., Nelson, A.: Phys. Rev. Lett. 82, 4971 (1999) ADSMathSciNetCrossRefGoogle Scholar
  24. Conde-Saavedra, G., Iribarrem, A., Ribeiro, M.B.: Physica A, 417, 332 (2015) ADSCrossRefGoogle Scholar
  25. Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006) ADSCrossRefGoogle Scholar
  26. Dabrowski, M.P., Denkiewicz, T.: Phys. Rev. D 79, 063521 (2009) ADSMathSciNetCrossRefGoogle Scholar
  27. Deffayet, C.: Phys. Lett. B 502, 199 (2001) ADSCrossRefGoogle Scholar
  28. Deffayet, C., Dvali, G., Gabadadze, G.: Phys. Rev. D 65, 044023 (2002) ADSMathSciNetCrossRefGoogle Scholar
  29. Del Campo, S., Fabris, J.C., Herrera, R., Zimdahl, W.: Phys. Rev. D 83(12), 123006 (2011) ADSCrossRefGoogle Scholar
  30. Dvali, G., Gabadadze, G., Porrati, M.: Phys. Lett. B 485, 208 (2000) ADSMathSciNetCrossRefGoogle Scholar
  31. Feng, C., et al.: Phys. Lett. B 665(2), 111–119 (2008) ADSCrossRefGoogle Scholar
  32. Frieman, J.A., Turner, M.S., Huterer, D.: Annu. Rev. Astron. Astrophys. 46, 385 (2008) ADSCrossRefGoogle Scholar
  33. Gallavotti, G.: Rev. Mod. Phys. 57, 471 (1985) ADSCrossRefGoogle Scholar
  34. Gastmans, R., Kallosh, R., Truffin, C.: Nucl. Phys. B 133, 417 (1978) ADSCrossRefGoogle Scholar
  35. Gong, Y.: Phys. Rev. D 70(6), 064029 (2004) ADSCrossRefGoogle Scholar
  36. Gonzalez, J., Guzman, F.: Phys. Rev. D 79, 121501 (2009) ADSCrossRefGoogle Scholar
  37. Guo, Z., Ohta, N., Tsujikawa, S.: Phys. Rev. D 76(2), 023508 (2007) ADSCrossRefGoogle Scholar
  38. Hao, W.: Commun. Theor. Phys. 52(4), 743 (2009) CrossRefGoogle Scholar
  39. Hilfer, R.: Applications of Fractional Calculus in Physics (2000) zbMATHCrossRefGoogle Scholar
  40. Hooft, G.: arXiv preprint gr-qc/9310026 (1993)
  41. Hsu, S.D.: Phys. Lett. B 594, 13 (2004) ADSCrossRefGoogle Scholar
  42. Hu, W., Sugiyama, N.: Astron. J. 471, 542 (1996) ADSCrossRefGoogle Scholar
  43. Huang, Q.G., Li, M.: J. Cosmol. Astropart. Phys. 2004(08), 013 (2004) CrossRefGoogle Scholar
  44. Ito, M.: Europhys. Lett. 71(5), 712 (2005) ADSCrossRefGoogle Scholar
  45. Jacobson, T.: Phys. Rev. Lett. 75, 1260 (1995) ADSMathSciNetCrossRefGoogle Scholar
  46. Jamil, M., Saridakis, E.N., Setare, M.: Phys. Lett. B 679(3), 172–176 (2009) ADSCrossRefGoogle Scholar
  47. Jawad, A.: Astrophys. Space Sci. 353(2), 691 (2014) ADSCrossRefGoogle Scholar
  48. Jawad, A., Majeed, A.: Astrophys. Space Sci. 356(2), 375 (2015) ADSCrossRefGoogle Scholar
  49. Jawad, A., Rani, S., Salako, I.G., Gulshan, F.: Int. J. Mod. Phys. D 26, 1750049 (2017) ADSCrossRefGoogle Scholar
  50. Karami, K., Jamil, M., Ghaffari, S., Fahimi, K., Myrzakulov, R.: Can. J. Phys. 91, 770 (2013) ADSCrossRefGoogle Scholar
  51. Khurshudyan, M.: Astrophys. Space Sci. 361, 232 (2016a) ADSCrossRefGoogle 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) ADSCrossRefGoogle 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) ADSMathSciNetCrossRefGoogle Scholar
  56. Krasinski, A.: Inhomogeneous cosmological models (1997 and 2006) Google Scholar
  57. Labini, F.S.: Astron. Astrophys. Trans. 19, 397 (2000) ADSCrossRefGoogle Scholar
  58. Labini, F.S.: Europhys. Lett. 96, 59001 (2011) ADSCrossRefGoogle Scholar
  59. Lemets, O., Yerokhin, D.: arXiv preprint arXiv:1202.3457 (2012)
  60. Lewis, A., Challinor, A., Lasenby, A.: Astrophys. J. 538, 473 (2000) ADSCrossRefGoogle 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) ADSMathSciNetCrossRefGoogle Scholar
  63. Li, M.: Phys. Lett. B 603, 1 (2004b) ADSMathSciNetCrossRefGoogle Scholar
  64. Li, M., Li, X., Wang, S., Wand, Y.: Commun. Theor. Phys. 56, 525 (2011) ADSCrossRefGoogle Scholar
  65. Li, M., Li, X.-D., Wang, S., Wang, Y.: Front. Phys., 8, 828 (2013a) CrossRefGoogle Scholar
  66. Li, Y.-H., Wang, S., Li, X.-D., Zhang, X.: J. Cosmol. Astropart. Phys. 2013, 033 (2013b) CrossRefGoogle Scholar
  67. Linde, A.D.: Phys. Lett. B 175, 395 (1986) ADSCrossRefGoogle Scholar
  68. Maartens, R., Koyama, K.: Living Rev. Relativ. 13, 5 (2010) ADSCrossRefGoogle 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) ADSCrossRefGoogle Scholar
  71. Nojiri, S., Odintsov, S.D.: Gen. Relativ. Gravit. 38, 1285 (2006) ADSCrossRefGoogle Scholar
  72. Nojiri, S., Odintsov, S.: Eur. Phys. J. C 77, 528 (2017) ADSCrossRefGoogle Scholar
  73. Nojiri, S., Odintsov, S.D., Sasaki, M.: Phys. Rev. D 71, 123509 (2005a) ADSCrossRefGoogle Scholar
  74. Nojiri, S., Odintsov, S.D., Tsujikawa, S.: Phys. Rev. D 71, 063004 (2005b) ADSCrossRefGoogle Scholar
  75. Padmanabhan, T.: Phys. Rep. 380, 235 (2003) ADSMathSciNetCrossRefGoogle Scholar
  76. Padmanabhan, T., Paranjape, A.: Phys. Rev. D 75, 064004 (2007) ADSMathSciNetCrossRefGoogle Scholar
  77. Paranjape, A., Sarkar, S., Padmanabhan, T.: Phys. Rev. D 74, 104015 (2006) ADSMathSciNetCrossRefGoogle Scholar
  78. Pavón, D., Wang, B.: Gen. Relativ. Gravit. 41(1), 1–5 (2009) ADSCrossRefGoogle Scholar
  79. Pavón, D., Zimdahl, W.: Phys. Lett. B 628(3), 206–210 (2005) ADSCrossRefGoogle Scholar
  80. Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003) ADSCrossRefGoogle Scholar
  81. Perlmutter, S., et al.: Astron. J. 517(2), 565 (1999) CrossRefGoogle Scholar
  82. Ribeiro, M.B., Miguelote, A.Y.: Braz. J. Phys. 28, 132 (1998) ADSCrossRefGoogle Scholar
  83. Riess, G., et al.: Astron. J. 116(3), 1009 (1998) ADSCrossRefGoogle Scholar
  84. Sadri, E., Vakili, B.: Astrophys. Space Sci. 363, 13 (2018) ADSCrossRefGoogle Scholar
  85. Sahni, V., Saini, T.D., Starobinsky, A.A., Alam, U.: JETP Lett. 77(5), 201–206 (2003) ADSCrossRefGoogle Scholar
  86. Sahni, V., Shafieloo, A., Starobinsky, A.A.: Phys. Rev. D 78(10), 103502 (2008) ADSCrossRefGoogle Scholar
  87. Salti, M., Korunur, M., Acikgoz, I.: Eur. Phys. J. Plus 129, 95 (2014) CrossRefGoogle 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) CrossRefGoogle Scholar
  90. Setare, M.: Phys. Lett. B 644(2), 99–103 (2007b) ADSMathSciNetCrossRefGoogle Scholar
  91. Setare, M., Saridakis, E.: Phys. Lett. B 671(3), 331–338 (2009a) ADSCrossRefGoogle Scholar
  92. Setare, M., Saridakis, E.: J. Cosmol. Astropart. Phys. 2009(03), 002 (2009b) CrossRefGoogle Scholar
  93. Alam, S., et al.: Mon. Not. R. Astron. Soc. 470, 2617–2652 (2017) ADSCrossRefGoogle Scholar
  94. Sheykhi, A.: J. Cosmol. Astropart. Phys. 2009(05), 019 (2009) CrossRefGoogle Scholar
  95. Sheykhi, A., Wang, B.: Mod. Phys. Lett. A 25, 1199 (2010) ADSCrossRefGoogle Scholar
  96. Sheykhi, A., Wang, B., Cai, R.G.: Phys. Rev. D 76(2), 023515 (2007a) ADSMathSciNetCrossRefGoogle Scholar
  97. Sheykhi, A., Wang, B., Cai, R.G.: Nucl. Phys. B 779(1), 1–12 (2007b) ADSCrossRefGoogle Scholar
  98. Sheykhi, A., Dehghani, M., Hosseini, S.: Phys. Lett. B 726, 23 (2013a) ADSCrossRefGoogle Scholar
  99. Sheykhi, A., Teimoori, Z., Wang, B.: Phys. Lett. B 718, 1203 (2013b) ADSCrossRefGoogle Scholar
  100. Sheykhi, A., Dehghani, M., Ghaffari, S.: Int. J. Mod. Phys. D 25(02), 1650018 (2016) ADSCrossRefGoogle Scholar
  101. Susskind, L.: J. Math. Phys. 36(11), 6377–6396 (1995) ADSMathSciNetCrossRefGoogle 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) ADSMathSciNetCrossRefGoogle 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) ADSCrossRefGoogle Scholar
  107. Wang, S., Wang, Y., Li, M.: arXiv preprint arXiv:1612.00345 (2016b)
  108. Wei, H.: Class. Quantum Gravity 29, 175008 (2012) ADSCrossRefGoogle Scholar
  109. Wei, H., Zhang, S.N.: Phys. Rev. D 76(6), 063003 (2007) ADSCrossRefGoogle 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) ADSCrossRefGoogle 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

Personalised recommendations