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Tsallis, Rényi and Sharma-Mittal holographic and new agegraphic dark energy models in D-dimensional fractal universe

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Abstract.

In this work, we explore the accelerated expansion of the Universe through a non-linear interaction of newly proposed dark energy models (namely Tsallis holographic dark energy (HDE), Rényi HDE, Sharma Mittal HDE, Tsallis new agegraphic dark energy (NADE), Rényi NADE and Sharma-Mittal NADE) with cold dark matter in the background of flat D -dimensional fractal Universe. The effect of IR cutoffs including the Hubble radius and Granda-Oliveros (GO) on the properties of the considered dark energy models have been investigated in this context. The cosmological parameters such as equation of state (EoS) parameter, squared speed of sound and \( \omega_{d}\) - \( \omega^{\prime}_{d}\) cosmological plane during the cosmic evolution have been calculated. Analyzing the behavior of such cosmological parameters graphically, it is found that the considered HDE and NADE models can lead to the late time accelerated expansion in the presence of interaction between two dark sectors of the Universe in more general space-time. This result is similar to the standard interacting HDE model with Hubble cutoff in FRW Universe.

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References

  1. A.G. Riess, A.V. Filippenko, P. Challis, A. Clocchiattia, A. Diercks, P.M. Garnavich, R.L. Gilliland, C.J. Hogan, S. Jha, R.P. Kirshner et al., Astron. J. 116, 1009 (1998)

    ADS  Google Scholar 

  2. S. Perlmutter, G. Aldering, G. Goldhaber, R.A. Knop, P. Nugent, P.G. Castro, S. Deustua, S. Fabbro, A. Goobar, D.E. Groom et al., Astron. J. 517, 565 (1999)

    Google Scholar 

  3. P. Bernardis, P.A.R. Ade, J.J. Bock, J.R. Bond, J. Borrill, A. Boscaleri, K. Coble, B.P. Crill, G. DeGasperis, P.C. Farese et al., Nature 404, 955 (2000)

    ADS  Google Scholar 

  4. S. Perlmutter, G. Aldering, R. Amanullah, P. Astier, G. Blanc, M.S. Burns, A. Conley, S.E. Deustua, M. Doi, R. Ellis et al., Astrophys. J. 598, 102 (2003)

    ADS  Google Scholar 

  5. M. Colless, G. Dalton, S. Maddox, W. Sutherland, P. Norberg, S. Cole, J.B. Hawthrone, T. Bridges, R. Cannon, C. Collins et al., Mon. Not. R. Astron. Soc. 328, 1039 (2001)

    ADS  Google Scholar 

  6. M. Tegmark, M.A. Strauss, M.R. Blanton, K. Abazajian, S. Dodelson, H. Sandvik, X. Wang, D.H. Weinberg, I. Zehavi, N.A. Bahcall et al., Phys. Rev. D 69, 103501 (2004)

    ADS  Google Scholar 

  7. S. Cole, W.J. Percival, R.A. Peacock, P. Norberg, C.M. Baugh, C.S. Frenk, I. Baldry, J. Bland-Hawthorn, T. Bridges, R. Cannon et al., Mon. Not. R. Astron. Soc. 362, 505 (2005)

    ADS  Google Scholar 

  8. V. Springel, C.S. Frenk, S.M.D. White, Nature 440, 1137 (2006)

    ADS  Google Scholar 

  9. S. Hanany, P. Ade, A. Balbi, J. Bock, J. Borrill, A. Boscaleri, P. Bernardis, P.G. Ferreira, V.V. Hristov, A.H. Jaffe et al., Astrophys. J. Lett. 545, L5 (2000)

    ADS  Google Scholar 

  10. C.B. Netterfield, P.A.R. Ade, J.J. Bock, J.R. Bond, J. Borrill, A. Boscaleri, K. Coble, C.R. Contaldi, B.P. Crill, P. Bernardis et al., Astrophys. J. 571, 604 (2002)

    ADS  Google Scholar 

  11. D.N. Spergel, L. Verde, H.V. Peiris, E. Komatsu, M.R. Nolta, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut et al., Astrophys. J. Suppl. 148, 175 (2003)

    ADS  Google Scholar 

  12. S. Nojiri, S.D. Odintsov, Phys. Lett. B 639, 144 (2006)

    ADS  Google Scholar 

  13. K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, Astrophys. Space Sci. 342, 155 (2012)

    ADS  Google Scholar 

  14. A. Sen, JHEP 065, 0207 (2002)

    Google Scholar 

  15. M. Malekjani, T. Naderi, F. Pace, Mon. Not. R. Acad. Sci. B 453, 4148 (2015)

    ADS  Google Scholar 

  16. T. Chiba, T. Okabe, M. Yamaguchi, Phys. Rev. D 62, 023511 (2000)

    ADS  Google Scholar 

  17. R. Myrzakulov, arXiv:1011.4337v4 [astro-ph.CO] (2010)

  18. S. Maity, U. Debnath, Astrophys. Space Sci. 345, 399 (2013)

    ADS  Google Scholar 

  19. S. Maity, U. Debnath, Eur. Phys. J. Plus 129, 14 (2014)

    Google Scholar 

  20. S. Nojiri, S.D. Odintsov, Phys. Lett. B 562, 147 (2003)

    ADS  Google Scholar 

  21. V. Pasquier, U. Moschella, A.Y. Kamenshchick, U. Moschella, V. Pasquier, Phys. Lett. B 511, 265 (2001)

    ADS  Google Scholar 

  22. S. Weinberg, Rev. Mod. Phys. 61, 1 (1998)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  24. T. Padmanabhan, Phys. Rep. 380, 235 (2003)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  26. S. Maity, U. Debnath, Int. J. Theor. Phys. 55, (2016)

  27. M.R. Setare, Phys. Lett. B 644, 99 (2007)

    ADS  MathSciNet  Google Scholar 

  28. A.D. Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010)

    ADS  Google Scholar 

  29. R. Ferraro, F. Fiorini, Phys. Lett. B 702, 75 (2011)

    ADS  MathSciNet  Google Scholar 

  30. P. Horava, Phys. Rev. D 79, 084008 (2009)

    ADS  MathSciNet  Google Scholar 

  31. P. Horava, JHEP 03, 020 (2009)

    ADS  MathSciNet  Google Scholar 

  32. P. Horava, Phys. Rev. Lett. 102, 161301 (2009)

    ADS  MathSciNet  Google Scholar 

  33. S. Maity, P. Rudra, arXiv:1802.00313v2 [gr-qc]

  34. C.H. Brans, R.H. Dicke, Phys. Rev. D 124, 925 (1961)

    ADS  Google Scholar 

  35. G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, S. Zerbini, Phys. Rev. D 73, 084007 (2006)

    ADS  Google Scholar 

  36. T. Harko, S.N. Francisco, F.S.N. Lobo, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 024020 (2011)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  39. P. Horava, D. Minic, Phys. Rev. Lett. 85, 1610 (2000)

    ADS  MathSciNet  Google Scholar 

  40. S. Thomas, Phys. Rev. Lett. 89, 081301 (2002)

    ADS  MathSciNet  Google Scholar 

  41. S.D.H. Hsu, Phys. Lett. B 594, 13 (2004)

    ADS  Google Scholar 

  42. B. Wang, E. Abdalla, F. Atrio-Barandela, D. Pavon, Rep. Prog. Phys. 79, 096901 (2016)

    ADS  Google Scholar 

  43. S. Wang, Y. Wang, M. Li, Phys. Rep. 699, 1 (2017)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  45. A. Sheykhi, Phys. Rev. D 84, 107302 (2011)

    ADS  Google Scholar 

  46. B. Hu, Y. Ling, Phys. Rev. D 73, 123510 (2006)

    ADS  Google Scholar 

  47. Y.Z. Ma, Y. Gong, X. Chen, Eur. Phys. J. C 60, 303 (2009)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  49. M.R. Setare, Astrophys. Space Sci. 326, 27 (2010)

    ADS  Google Scholar 

  50. K. Saaidi, H. Sheikhahmadi, A.H. Mohammadi, Astrophys. Space Sci. 338, 355 (2012)

    ADS  Google Scholar 

  51. J.F. Zhang, Y.H. Lee, X. Zhang, Eur. Phys. J. C 73, 2280 (2013)

    ADS  Google Scholar 

  52. M. Tavayef, A. Sheykhi, K. Bamba, H. Moradpour, Phys. Lett. B 781, 195 (2018)

    ADS  Google Scholar 

  53. H. Moradpour, S.A. Moosavi, I.P. Lobo, J.P.M. Graca, A. Jawad, I.G. Salako, Eur. Phys. J. C 829, 78 (2018)

    Google Scholar 

  54. A.S. Jahromi, S.A. Moosavi, H. Moradpour, J.P.M. Grac, I.P. Lobo, I.G. Salako, A. Jawad, Phys. Lett. B 780, 21 (2018)

    ADS  MathSciNet  Google Scholar 

  55. C. Tsallis, L.J.L. Cirto, Eur. Phys. J. C 73, 2487 (2013)

    ADS  Google Scholar 

  56. A. Sayahian Jahromi et al., Phys. Lett. B 780, 21 (2018)

    ADS  MathSciNet  Google Scholar 

  57. C. Tsallis, J. Stat. Phys. 52, 479 (1988)

    ADS  Google Scholar 

  58. A. Rényi, in Proceedings of the 4th Berkely Symposium on Mathematics, Statistics and Probability (University California Press, Berkeley, CA, 1961) pp. 547--561

  59. B.D. Sharma, D.P. Mittal, J. Math. Sci. 10, 28 (1975)

    MathSciNet  Google Scholar 

  60. M. Sharif, S. Saba, Symmetry 11, 92 (2019)

    Google Scholar 

  61. S. Ghaffari, H. Moradpour, J.P.M. Graa, V.B. Bezerra, I.P. Lobo, Phys. Dark Universe 23, 100246 (2019)

    ADS  Google Scholar 

  62. S. Ghaffari, H. Moradpour, I.P. Lobo, J.P.M. Graa, V.B. Bezerra, Eur. Phys. J. C 78, 706 (2018)

    ADS  Google Scholar 

  63. M.A. Zadeh, A. Sheykhi, H. Moradpour, Mod. Phys. Lett. A 34, 1950086 (2019)

    ADS  Google Scholar 

  64. M.A. Zadehl, A. Sheykhi, H. Moradpour, K. Bamba, Eur. Phys. J. C 78, 940 (2018)

    ADS  Google Scholar 

  65. A. Jawad, K. Bamba, M. Younas, S. Qummer, S. Rani, Symmetry 10, 635 (2018)

    Google Scholar 

  66. G. Calcagni, JHEP 03, 120 (2010)

    ADS  Google Scholar 

  67. S. Maity, U. Debnath, Int. J. Theor. Phys. 55, 2668 (2016)

    Google Scholar 

  68. U. Debnath, K. Bamba, arXiv:1902.01397v1 [gr-qc]

  69. M. Roos, Introduction to Cosmology (John Wiley and Sons, UK, 2003)

  70. F. Arevalo, A.P.R. Bacalhau, W. Zimdahl, Class. Quantum Grav. 29, 235001 (2012)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  72. L.N. Granda, A. Oliveros, Phys. Lett. B 669, 275 (2008)

    ADS  Google Scholar 

  73. L.N. Granda, A. Oliveros, Phys. Lett. B 671, 199 (2009)

    ADS  Google Scholar 

  74. H. Moradpour, S.A. Moosavi, I.P. Lobo, J.P.M. Graca, A. Jawad, I.G. Salako, Eur. Phys. J. C 829, 78 (2018)

    Google Scholar 

  75. A.G. Cohen, D.B. Kaplan, A.E. Nelson, Phys. Rev. Lett. 82, 4971 (1999)

    ADS  MathSciNet  Google Scholar 

  76. M.A. Zadeh, A. Sheykhi, H. Moradpur, Mod. Phys. Lett. A 34, 1950086 (2019)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Techno India Salt Lake, Sector-V, 700 091, Kolkata, India

    Sayani Maity

  2. Department of Mathematics, Indian Institute of Engineering Science and Technology, 711103, Shibpur, Howrah, India

    Ujjal Debnath

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  1. Sayani Maity
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  2. Ujjal Debnath
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Correspondence to Sayani Maity.

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Maity, S., Debnath, U. Tsallis, Rényi and Sharma-Mittal holographic and new agegraphic dark energy models in D-dimensional fractal universe. Eur. Phys. J. Plus 134, 514 (2019). https://doi.org/10.1140/epjp/i2019-12884-6

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