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Viscous Ricci Dark Energy Cosmological Models in Brans-Dicke Theory

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The whole article deals with the analysis of the cosmic model of Ruban’s space-time in the context of a bulk viscosity impact in the form of Ricci dark energy within the framework Brans-Dicke theory. We believe that outer space is filled with dark matter and viscous Ricci dark energy (VRDE) under the pressureless situation. The velocity and rate at which the Universe is expanding are presumed to be proportional to the coefficient of total bulk viscosity, is in the form, \({\upxi }_{0}+{\upxi }_{1}\dot{a}/a+{\upxi }_{2}\ddot{a}/a,\) where \({\upxi }_{0},{\upxi }_{1}\) and \({\upxi }_{2}\) are the constants. To solve the RDE model's field equations, we utilize the relation among the metric potentials and also the power-law relation among the average scale factor a(t) and scalar field ϕ. To examine the evolutionary dynamics of the Universe, we investigate the deceleration parameter q, jerk parameter j, EoS parameter \({\upomega }_{de},\) Om(z) , stability of the obtained models through the square speed of the sound \({v}_{s}^{2},{\upomega }_{de}-{\omega }_{de}{\prime}\) plane, statefinder parameter planes (r, s) and (q, r) and presented via graphical representation. By the end of the discussion, VRDE model was found to be compatible with the present accelerated expansion of the Universe.

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References

  1. S. Nojiri, S. D. Odintsov, Phys. Rep., 505, 59, 2011.

    Article  ADS  MathSciNet  Google Scholar 

  2. S. Nojiri et al., Phys. Rep., 692, 1, 2017.

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Einstein, Sitzungsber. Preuss. Akad. Wiss, Berlin (Math. Phys. ), 142, 1917.

  4. A. G. Riess et al., Astron. J., 116, 1009, 1998.

    Article  ADS  Google Scholar 

  5. S. Perlmutter et al., Nature, 391, 51, 1998.

    Article  ADS  Google Scholar 

  6. S. Perlmutter et al., Astrophys. J., 517, 565, 1999.

    Article  ADS  Google Scholar 

  7. C. L. Bennet et al., Astrophys. J. Suppl., 148, 1, 2003.

    Article  ADS  Google Scholar 

  8. M. Tegmark et al., Phys. Rev. D, 69, 103501, 2004.

    Article  ADS  Google Scholar 

  9. J. Silk, Ann. Phys. (Berlin), 15, 75, 2006.

    Article  ADS  MathSciNet  Google Scholar 

  10. L. Bergstrom, Ann. Phys. (Berlin), 524, 479, 2012.

    Article  ADS  Google Scholar 

  11. C. S. Frenk, S. D. M. White, Ann. Phys. (Berlin), 524, 507, 2012.

    Article  ADS  Google Scholar 

  12. M. Vogelsberger et al., Mon. Not. Roy. Astron. Soc., 460, 1399, 2016.

    Article  ADS  Google Scholar 

  13. S. Nojiri et al., Phys. Rev. D, 71, 063004, 2005b. arXiv:hep-th/0501025.

    Article  ADS  Google Scholar 

  14. S. Nojiri, S. D. Odintsov, Phys. Rev. D, 72, 023003, 2005a. arXiv: hep-th/0505215.

    Article  ADS  Google Scholar 

  15. H. Stefancic, Phys. Rev. D, 71, 084024, 2005. arXiv:astro-ph/ 0411630.

    Article  ADS  Google Scholar 

  16. S. Weinberg, Rev. Mod. Phys., 61, 1, 1989.

    Article  ADS  Google Scholar 

  17. K. Bamba et al., Astrophys. Space Sci., 342, 155, 2012.

    Article  ADS  Google Scholar 

  18. S. M. Carroll, Phys. Rev. Lett., 81, 3067, 1998.

    Article  ADS  Google Scholar 

  19. T. Chiba et al., Phys. Rev. D, 62, 023511, 2000.

    Article  ADS  Google Scholar 

  20. A. Kamenshchik et al., Phys. Lett. B, 511, 265, 2001.

    Article  ADS  Google Scholar 

  21. G. 't Hooft, arXiv:gr-qc/9310026, 1993.

  22. L. Susskind, J. Math. Phys., 36, 6377, 1995.

    Article  ADS  MathSciNet  Google Scholar 

  23. H. Wei, R. G. Cai, Phys. Lett. B, 660, 113, 2008.

    Article  ADS  Google Scholar 

  24. S. Capozziello, Int. J. Mod. Phys. D, 11, 483, 2002.

    Article  ADS  Google Scholar 

  25. L. Amendola, Phys. Rev. D, 60, 043501, 1999.

    Article  ADS  Google Scholar 

  26. C. Brans, R. H. Dicke, Phys. Rev., 124, 925, 1961.

    Article  ADS  MathSciNet  Google Scholar 

  27. C. M. Will, Living Rev. Relativ., 17, 4, 2014.

    Article  ADS  Google Scholar 

  28. O. Bertolami, P. J. Martins, Phys. Rev. D, 61, 064007, 2000.

    Article  ADS  Google Scholar 

  29. L. Qiang et al., Phys. Rev. D, 71, 061501, 2005.

    Article  ADS  Google Scholar 

  30. Y. Bisabr, Gen. Relativ. Gravit., 44, 427, 2012.

    Article  ADS  MathSciNet  Google Scholar 

  31. X. L. Liu, X. Zhang, Commun. Theor. Phys., 52, 761, 2009.

    Article  ADS  Google Scholar 

  32. B. Bertotti et al., Nature (London), 425, 374, 2003.

    Article  ADS  Google Scholar 

  33. C. Mathiazhagan, V. B. Johri, Class. Quant. Grav., 1, L29, 1984.

    Article  ADS  Google Scholar 

  34. V. Acquaviva, L. Verde, J. Cosmol. Astropart. Phys., 0712, 001, 2007.

    Article  ADS  Google Scholar 

  35. S. Tsujikawa et al., Phys. Rev. D, 77, 103009, 2008.

    Article  ADS  Google Scholar 

  36. F. Wu, X. Chen, Phys. Rev. D, 82, 083003, 2010.

    Article  ADS  Google Scholar 

  37. F. Wu, X. Chen, Phys. Rev. D, 88, 084053, 2013.

    Article  ADS  Google Scholar 

  38. R. Prasad et al., Eur. Phys. J. Plus., 135, 297, 2020.

    Article  Google Scholar 

  39. S. P. Hatkar et al., Astrophys. Space Sci., 365 7, 2020.

    Article  ADS  MathSciNet  Google Scholar 

  40. A. Y. Shaikh, Bulg. J. Phys., 47, 43, 2020.

    Google Scholar 

  41. K. Koyama, Phys. Rev. D, 102, 021502(R), 2020.

    Article  ADS  Google Scholar 

  42. M. Sharif, A. Majid, Phys. Dark Universe, 30, 100610, 2020.

    Article  Google Scholar 

  43. S. S. Singh, Y. Soibam, Int. J. Geom. Methods Mod. Phys., 18, 2150141, 2021.

    Article  Google Scholar 

  44. S. Hou, Astron. Nachr., 342, 96, 2021.

    Article  ADS  Google Scholar 

  45. S. Roy et al., World Sci. News, 145, 159, 2021.

    Google Scholar 

  46. M. Sharif, A. Majid, Phys. Dark Universe, 32 100803, 2021.

    Article  Google Scholar 

  47. S. Tahura et al., Phys. Rev. D, 103, 104026, 2021.

    Article  ADS  MathSciNet  Google Scholar 

  48. M. V. Santhi, Y. S. Babu, New Astron., 1384, 2022.

  49. M. V. Santhi et al., Advances in Astronomy, https://doi.org/10.1155/2022/5364541, 2022.

  50. M. Srivastava, C. P. Singh, Inter. J. G. M. in. Modern Phys., 8, 55, 2018.

    Google Scholar 

  51. C. P. Singh, Simran Kaur Phys. Rev. D, 100, 084057, 2019.

    Article  ADS  MathSciNet  Google Scholar 

  52. X. Gao et al., Phys. Lett. B, 795, 144, 2019.

    Article  ADS  MathSciNet  Google Scholar 

  53. S. D. H. Hsu, Phys. Lett. B, 594, 13, 2004.

    Article  ADS  Google Scholar 

  54. R. Bousso, Class. Quant. Grav., 17, 997, 2000.

    Article  ADS  Google Scholar 

  55. M. Li, Phys. Lett. B, 603, 1, 2004.

    Article  ADS  Google Scholar 

  56. M. Li et al., J. Cosmol. Astropart. Phys., 06, 036, 2009.

    Article  ADS  Google Scholar 

  57. C. Gao et al., Phys. Rev. D, 79, 043511, 2009.

    Article  ADS  Google Scholar 

  58. S. Nojiri, S. D. Odintsov, Gen. Relat. Gravit., 38, 1285, 2006.

    Article  ADS  Google Scholar 

  59. C. J. Feng, X. Z. Li, Phys. Lett. B, 680, 355, 2009.

    Article  ADS  Google Scholar 

  60. A. Dixit et al., Walailak J. Sci. and Tech., 18(3), 6986, 2021.

    Article  Google Scholar 

  61. S. Chakrabarti et al., Canadian Journal of Physics, 0248, R1, 2019.

    Google Scholar 

  62. A. Kumar, C. P. Singh, Pramana, J. Phys., 94, 129, 2020.

    Google Scholar 

  63. A. Kumar, C. P. Singh, Eur. Phys. J. Plus, 136, 820, 2021.

    Article  Google Scholar 

  64. C. P. Singh, A. Kumar, Eur. Phys. J. Plus, 133, 312, 2018.

    Article  Google Scholar 

  65. C. P. Singh, A. Kumar, Astrophys Space Sci., 364, 94, 2019.

    Article  ADS  Google Scholar 

  66. M. V. Santhi, Y. S. Babu, Indian J. Phys., doi. org/10. 1007/s12648-021-02121-1, 2021.

  67. A. Sasidharan, T. K. Mathew, Eur. Phys. J. C, 75, 348, 2015.

    Article  ADS  Google Scholar 

  68. C. Eckart, Phys. Rev., 58, 919, 1940.

    Article  ADS  Google Scholar 

  69. L. D. Landau, E. M. Lifshitz, Phys. Lett. B, 603, 1, 1987.

    Google Scholar 

  70. W. Israel, Stewart, J. M. : Phys. Lett. A, 58, 213, 1976.

    ADS  Google Scholar 

  71. M. Cataldo et al., Phys. Lett. B, 619, 5, 2005.

    Article  ADS  Google Scholar 

  72. J. D. Barrow, Phys. Lett. B, 180, 335, 1987.

    Article  ADS  Google Scholar 

  73. I. Brevik, S. D. Odintsov, Phys. Rev. D, 65, 067302, 2002.

    Article  ADS  MathSciNet  Google Scholar 

  74. D. J. Liu, X. Z. Li, Phys. Lett. B, 611, 8, 2005.

    Article  ADS  Google Scholar 

  75. I. Brevik et al., Int. J. Mod. Phys. D, 26, 1730024, 2017.

    Article  ADS  Google Scholar 

  76. I. Brevik et al., Int. J. Geom. Methods Mod. Phys., 14, 1750185, 2017.

    Article  MathSciNet  Google Scholar 

  77. M. V. Santhi et al., Indian J. Phys., 97 1641, 2023.

    Article  ADS  Google Scholar 

  78. J. Ren, X. H. Meng, Phys. Lett. B, 633, 1, 2006.

    Article  ADS  Google Scholar 

  79. A. Tawfik, T. Harko, Phys. Rev. D, 85, 084032, 2012.

    Article  ADS  Google Scholar 

  80. C. P. Singh, P. Kumar, Eur. Phys. J. C, 74, 3070, 2014.

    Article  ADS  Google Scholar 

  81. C. P. Singh, P. Kumar, Astrophys. Space Sci., 361, 157, 2016.

    Article  ADS  Google Scholar 

  82. S. Nojiri, S. D. Odintsov, Phys. Rev. D, 72 023003, 2005.

    Article  ADS  Google Scholar 

  83. S. Capozziello et al., Phys. Rev. D, 73 043512, 2006.

    Article  ADS  Google Scholar 

  84. W. Steven, Astrophys. J., 168, 1971.

  85. N. Caderni, R. Fabbri, Phys. Rev. D, 20, 1251, 1979.

    Article  ADS  Google Scholar 

  86. O. Heckmann et al., Wiley New York, 438, 1962.

  87. P. Szekeres, Commun. Math. Phys., 41, 55, 1975.

    Article  ADS  Google Scholar 

  88. D. A. Szafron, J. Math. Phys., 18, 1673, 1977.

    Article  ADS  MathSciNet  Google Scholar 

  89. M. D. Pollock, N. Caderni, Mon. Not. R. Astron. Soc., 190, 509, 1980.

    Article  ADS  Google Scholar 

  90. S. W. Goode, J. Wainwright, Phys. Rev. D, 26, 3315, 1982.

    Article  ADS  MathSciNet  Google Scholar 

  91. J. A. S. Lima, Phys. Lett. A, 116, 210, 1986.

    Article  ADS  MathSciNet  Google Scholar 

  92. B. Raj, G. Singh, Astrophys. Space Sci., 138, 71, 1987.

    Article  ADS  MathSciNet  Google Scholar 

  93. W. B. Bonnor et al., Gen. Relativ. Gravit., 549, 1977.

  94. T. Nazira, W. Ioav, Astrophys. J., 317, 52, 1987.

  95. 94. T. Nazira, W. Ioav, Astrophys. J., 317, 52, 1987.

    Article  MathSciNet  Google Scholar 

  96. V. A. Ruban, J. Exp. Theo. Phys. Lett., 29, 1969.

  97. J. A. S. Lima, M. A. S. Nobre, Class. Quant. Grav., 7, 1990.

  98. 97. J. A. S. Lima, T. Jayme, Gen. Relativ. Gravit., 20, 1019, 1988.

    Article  ADS  Google Scholar 

  99. J. A. S. Lima, T. Jayme, Class. Quant. Gravit., 6, 1989.

  100. V. G. Mete et al., IOSR J. Math., 25, 2015.

  101. 100. C. Aktaº, Inter. J. M. Phys. A, 34, 1950011, 2019.

    Google Scholar 

  102. 101. M. V. Santhi, T. C. Naidu, New Astron., 92 101725, 2022.

    Article  Google Scholar 

  103. 102. W. Zimdahl, Phys. Rev. D, 53, 5483, 1996.

    Article  ADS  Google Scholar 

  104. 103. C. Eckart, Phys. Rev., 58, 919, 1940.

    Article  ADS  Google Scholar 

  105. 104. C. B. Collins et al., Gen. Relativ. Gravit., 12, 805, 1980.

    Article  ADS  Google Scholar 

  106. 105. K. S. Thorne, Astrophys. J. 148, 51, 1967.

    Article  ADS  Google Scholar 

  107. 106. S. K. Tripathy et al., Eur. Phys. J. C, 75, 149, 2015.

    Article  ADS  Google Scholar 

  108. 107. M. V. Santhi, T. C. Naidu, Indian J. Phys., 96, 953, 2022.

    Article  ADS  Google Scholar 

  109. 108. M. V. Santhi, T. C. Naidu, Afr. Mat., 33, 98, 2022.

    Article  Google Scholar 

  110. 109. M. Visser, Gen. Relativ. Grav., 37, 1541, 2005.

    Article  ADS  Google Scholar 

  111. 110. D. Rapetti et al., Mon. Not. Roy. Astron. Soc., 375, 1510, 2007.

    Article  ADS  Google Scholar 

  112. 111. V. Sahni et al., J. Exp. Theor. Phys. Lett., 77, 201, 2003.

    Article  Google Scholar 

  113. 112. U. Alam et al., Mon. Not. Roy. Astron. Soc., 344, 1057, 2003.

    Article  ADS  Google Scholar 

  114. 113. N. Aghanim et al., [Plancks Collaboration], 2018, Astron. Astrophys., 641, A6 2020.

    Google Scholar 

  115. 114. R. Caldwell, E. V. Linder, Phys. Rev. Lett., 95, 141301, 2005.

    Article  ADS  Google Scholar 

  116. 115. V. Sahni et al., Phys. Rev. D, 78, 103502, 2008.

    Article  ADS  Google Scholar 

  117. 116. Y. S. Myung, Phys. Lett. B, 652, 223, 2007.

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Andhra University, Visakhapatnam, 530003, India

    M. Vijaya Santhi, T. Chinnappalanaidu & S. Srivani Madhu

  2. Department of Mathematics, Vignan’s Institute of Information Technology(Autonomous), Visakhapatnam, 530049, India

    T. Chinnappalanaidu

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  1. M. Vijaya Santhi
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  2. T. Chinnappalanaidu
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  3. S. Srivani Madhu
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Correspondence to M. Vijaya Santhi.

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Published in Astrofizika, Vol. 66, No. 4, pp. 603-631 (November 2023).

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Vijaya Santhi, M., Chinnappalanaidu, T. & Srivani Madhu, S. Viscous Ricci Dark Energy Cosmological Models in Brans-Dicke Theory. Astrophysics 66, 559–589 (2023). https://doi.org/10.1007/s10511-024-09810-9

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