• [1]

    B. P. Abbott and et al. (Virgo and LIGO Scientific Collaborations), Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837[gr-qc

  • [2]

    K. Akiyama and et al. (Event Horizon Telescope Collaboration), Astrophys. J. 875, L1 (2019), arXiv:1906.11238[astro-ph.GA

  • [3]

    K. Akiyama and et al. (Event Horizon Telescope Collaboration), Astrophys. J. 875, L6 (2019), arXiv:1906.11243[astro-ph.GA

  • [4]

    N. Cruz, M. Olivares, and J. R. Villanueva, Class. Quantum Grav. 22, 1167 (2005), arXiv:gr-qc/0408016

  • [5]

    Z. Stuchlık and J. Schee, Journal of Cosmology and Astroparticles 9, 018 (2011)

  • [6]

    C. Grenon and K. Lake, Phys. Rev. D 81, 023501 (2010), arXiv:0910.0241[astro-ph.CO

  • [7]

    L. Rezzolla, O. Zanotti, and J. A. Font, Astronomy and Astrophysics 412, 603 (2003), arXiv:gr-qc/0310045

  • [8]

    I. Arraut, Int. J. Mod. Phys. D 24, 1550022 (2015)

  • [9]

    V. Faraoni, ed., Lecture Notes in Physics, Berlin Springer Verlag, Lecture Notes in Physics, Berlin Springer Verlag, Vol. 907 (2015)

  • [10]

    S. Shaymatov, B. Ahmedov, Z. Stuchlık et al., International Journal of Modern Physics D 27, 1850088 (2018)

  • [11]

    P. J. Peebles and B. Ratra, Rev. of Mod. Phys. 75, 559 (2003), arXiv:astro-ph/0207347

  • [12]

    C. Wetterich, Nucl. Phys. B 302, 668 (1988)

  • [13]

    R. Caldwell and M. Kamionkowski, Nature 458, 587 (2009)

  • [14]

    V. V. Kiselev, Class. and Quantum Grav. 20, 1187 (2003), arXiv:gr-qc/0210040[gr-qc

  • [15]

    S. Hellerman, N. Kaloper, and L. Susskind, Journal of High Energy Physics 2001, 003 (2001), arXiv:hepth/0104180[hep-th

  • [16]

    J. d. M. Toledo and V. B. Bezerra, Eur. Phys. J. C 78, 534 (2018)

  • [17]

    M. Batool and I. Hussain, International Journal of Modern Physics D 26, 1741005 (2017)

  • [18]

    G. Mustafa and I. Hussain, Eur. Phys. J. C 81, 419 (2021)

  • [19]

    M. Fathi, M. Olivares, and J. R. Villanueva, (2022), arXiv: 2205.13261[grqc]

  • [20]

    K. Hioki and K.-I. Maeda, Phys. Rev. D 80, 024042 (2009)

  • [21]

    F. Atamurotov, A. Abdujabbarov, and B. Ahmedov, Astrophys. Space Sci. 348, 179 (2013)

  • [22]

    F. Atamurotov, A. Abdujabbarov, and B. Ahmedov, Phys. Rev. D 88, 064004 (2013)

  • [23]

    A. Abdujabbarov, F. Atamurotov, Y. Kucukakca et al., Astrophys. Space. Sci. 344, 429 (2013), arXiv:1212.4949[physics.gen-ph

  • [24]

    F. Atamurotov, S. G. Ghosh, and B. Ahmedov, Eur. Physi. J. C 76, 273 (2016), arXiv:1506.03690[gr-qc

  • [25]

    U. Papnoi, F. Atamurotov, S. G. Ghosh et al., Phys. Rev. D 90, 024073 (2014), arXiv:1407.0834[gr-qc

  • [26]

    A. Abdujabbarov, F. Atamurotov, N. Dadhich et al., Eur. Phys. J. C 75, 399 (2015), arXiv:1508.00331[gr-qc

  • [27]

    R. Kumar and S. G. Ghosh, J. Cosmol. A. P. 2020, 053 (2020)

  • [28]

    P. V. P. Cunha, N. A. Eir′o, C. A. R. Herdeiro et al., J. Cosmol. A. P. 2020, 035 (2020), arXiv:1912.08833[gr-qc

  • [29]

    P. V. P. Cunha, C. A. R. Herdeiro, B. Kleihaus et al., Phys. Lett. B 768, 373 (2017), arXiv:1701.00079[gr-qc

  • [30]

    F. Atamurotov, U. Papnoi, and K. Jusufi, Class. Quan. Grav. 39, 025014 (2022), arXiv:2104.14898[gr-qc

  • [31]

    K. Jafarzade, M. Kord Zangeneh, and F. S. N. Lobo, J. Cosmol. A. P. 2021, 008 (2021), arXiv:2010.05755[gr-qc

  • [32]

    M. Afrin, R. Kumar, and S. G. Ghosh, Mon. Not. R. Astron. Soc. 504, 5927 (2021), arXiv:2103.11417[gr-qc

  • [33]

    M. Ghasemi-Nodehi, M. Azreg-A ınou, K. Jusufi et al., Phys. Rev. D 102, 104032 (2020), arXiv:2011.02276[gr-qc

  • [34]

    C. Bambi, K. Freese, S. Vagnozzi et al., Phys. Rev. D 100, 044057 (2019), arXiv:1904.12983[grqc

  • [35]

    S. Vagnozzi and L. Visinelli, Phys. Rev. D 100, 024020 (2019), arXiv:1905.12421[gr-qc

  • [36]

    M. Khodadi, A. Allahyari, S. Vagnozzi et al., JCAP 09, 026 (2020), arXiv:2005.05992[gr-qc

  • [37]

    K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D. 62, 084003 (2000)

  • [38]

    ?a. Bozza, S. Capozziello, G. Iovane et al., Gen. Rel. Grav. 33, 1535 (2001)

  • [39]

    â. Bozza, Phys. Rev. D. 66, 103001 (2002)

  • [40]

    S.-S. Zhao and Y. Xie, Phys. Lett. B. 774, 357 (2017)

  • [41]

    S. E. Vázquez and E. P. Esteban, Nuovo Cim. B 119, 489 (2004)

  • [42]

    E. F. Eiroa, G. E. Romero, and D. F. Torres, Phys. Rev. D. 66, 024010 (2002)

  • [43]

    E. F. Eiroa and D. F. Torres, Phys. Rev. D. 69, 063004 (2004)

  • [44]

    S. Chakraborty and S. Soumitra, J. Cosmol. A. P. 07, 045 (2017)

  • [45]

    V. Perlick, Living Reviews in Relativity 7, 9 (2004)

  • [46]

    A. Abdujabbarov, B. Ahmedov, N. Dadhich et al., Phys. Rev. D. 96, 084017 (2017)

  • [47]

    S. U. Islam, R. Kumar, and S. G. Ghosh, JCAP 2020, 030 (2020), arXiv:2004.01038[gr-qc

  • [48]

    K. S. Virbhadra and G. F. R. Ellis, Phys. Rev. D. 65, 103004 (2002)

  • [49]

    R. Kumar, S. U. Islam, and S. G. Ghosh, Eur. Phys. J. C 80, 1128 (2020), arXiv:2004.12970[gr-qc

  • [50]

    B. Narzilloev, S. Shaymatov, I. Hussain et al., Eur. Phys. J. C 81, 849 (2021), arXiv:2109.02816[gr-qc

  • [51]

    G. S. Bisnovatyi-Kogan and O. Y. Tsupko, Mon. Not. R. Astron. Soc. 404, 1790 (2010)

  • [52]

    G. Z. Babar, F. Atamurotov, and A. Z. Babar, Physics of the Dark Universe 32, 100798 (2021)

  • [53]

    V. Morozova, B. Ahmedov, and A. Tursunov, Astrophys. Space. Sci. 346, 513 (2013)

  • [54]

    G. Z. Babar, F. Atamurotov, S. Ul Islam et al., Phys. Rev. D 103, 084057 (2021), arXiv:2104.00714[gr-qc

  • [55]

    A. Hakimov and F. Atamurotov, Astrophys. Space. Sci. 361, 112 (2016)

  • [56]

    A. Rogers, Mon. Not. R. Astron. Soc. 451, 17 (2015)

  • [57]

    F. Atamurotov, A. Abdujabbarov, and J. Rayimbaev, Eur. Phys. J. C. 81, 118 (2021)

  • [58]

    C. Benavides-Gallego, A. Abdujabbarov, and Bambi, Eur. Phys. J. C. 78, 694 (2018)

  • [59]

    F. Atamurotov, S. Shaymatov, and B. Ahmedov, Galaxies 9, 54 (2021)

  • [60]

    F. Atamurotov, S. Shaymatov, P. Sheoran et al., J. Cosmol. P. A. 2021, 045 (2021), arXiv:2105.02214[gr-qc

  • [61]

    F. Atamurotov, F. Sarikulov, A. Abdujabbarov et al., Eur. Phys. J. Plus 137, 336 (2022)

  • [62]

    F. Atamurotov, F. Sarikulov, V. Khamidov et al., Eur. Phys. J. Plus 137, 567 (2022)

  • [63]

    F. Atamurotov and S. G. Ghosh, Eur. Phys. J. Plus 137, 662 (2022)

  • [64]

    F. Atamurotov, M. Alloqulov, A. Abdujabbarov et al., Eur. Phys. J. Plus 137, 634 (2022)

  • [65]

    G. W. Gibbons and M. C. Werner, Class. Quant. Grav. 25, 235009 (2008), arXiv:0807.0854[gr-qc

  • [66]

    M. C. Werner, Gen. Relativ. Gravit. 44, 3047 (2012)

  • [67]

    A. Ishihara, Y. Suzuki, T. Ono, et al., Phys. Rev. D 94, 084015 (2016)

  • [68]

    A. Ishihara, Y. Suzuki, T. Ono et al., Phys. Rev. D 95, 044017 (2017)

  • [69]

    T. Ono, A. Ishihara, and H. Asada, Phys. Rev. D 96, 104037 (2017)

  • [70]

    Z. Li and A. Övgün, Phys. Rev. D 101, 024040 (2020)

  • [71]

    Z. Li, G. Zhang, and A. Övgün, Phys. Rev. D 101, 124058 (2020)

  • [72]

    G. Crisnejo and E. Gallo, Phys. Rev. D 97, 124016 (2018), arXiv:1804.05473[gr-qc

  • [73]

    A. Övgün, Phys. Rev. D 98, 044033 (2018), arXiv:1805.06296[gr-qc

  • [74]

    A. Övgün, Phys. Rev. D 99, 104075 (2019), arXiv:1902.04411[gr-qc

  • [75]

    A. Övgün, Universe 5, 115 (2019), arXiv:1806.05549[physics.gen-ph

  • [76]

    W. Javed, J. Abbas, and A. Övgün, Eur. Phys. J. C 79, 694 (2019), arXiv:1908.09632[physics.gen-ph

  • [77]

    W. Javed, j. Abbas, and A. Övgün, Phys. Rev. D 100, 044052 (2019), arXiv:1908.05241[gr-qc

  • [78]

    W. Javed, R. Babar, and A. Övgün, Phys. Rev. D 100, 104032 (2019), arXiv:1910.11697[gr-qc

  • [79]

    W. Javed, A. Hamza, and A. Övgün, Phys. Rev. D 101, 103521 (2020), arXiv:2005.09464[gr-qc

  • [80]

    W. Javed, R. Babar, and A. Övgün, Phys. Rev. D 99, 084012 (2019), arXiv:1903.11657[gr-qc

  • [81]

    A. Övgün, I. Sakallı, and J. Saavedra, Annals Phys. 411, 167978 (2019), arXiv:1806.06453[gr-qc

  • [82]

    W. Javed, J. Abbas, and A. Övgün, Annals Phys. 418, 168183 (2020), arXiv:2007.16027[gr-qc

  • [83]

    R. C. Pantig and E. T. Rodulfo, Chin. J. Phys. 66, 691 (2020)

  • [84]

    R. C. Pantig, P. K. Yu, E. T. Rodulfo et al., Annals of Phys. 436, 168722 (2022)

  • [85]

    R. C. Pantig and A. Övgün, Eur. Phys. J. C 82, 391 (2022)

  • [86]

    M. Okyay and A. Övgün, JCAP 01, 009 (2022)

  • [87]

    H. Arakida, Gen. Rel. Grav. 50, 48 (2018), arXiv:1708.04011[gr-qc

  • [88]

    H. Arakida, JCAP 08, 028 (2021), arXiv:2006.13435[grqc

  • [89]

    Z. Zhang, Class. Quant. Grav. 39, 015003 (2022), arXiv:2112.04149[gr-qc

  • [90]

    Z. Li and J. Jia, Phys. Rev. D 104, 044061 (2021), arXiv:2108.05273[gr-qc

  • [91]

    I. D. D. Carvalho, G. Alencar, W. M. Mendes, and R. R. Landim, EPL 134, 51001 (2021), arXiv:2103.03845[grqc

  • [92]

    M. S. Ali and S. Kauhsal, Phys. Rev. D 105, 024062 (2022), arXiv:2106.08464[gr-qc

  • [93]

    Q.-M. Fu, L. Zhao, and Y.-X. Liu, Phys. Rev. D 104, 024033 (2021), arXiv:2101.08409[gr-qc

  • [94]

    R. Kumar, S. G. Ghosh, and A. Wang, Phys. Rev. D 100, 124024 (2019), arXiv:1912.05154[gr-qc

  • [95]

    K. Jusufi, A. Övgün, J. Saavedra, Y. Vásquez, and P. A. González, Phys. Rev. D 97, 124024 (2018), arXiv:1804.00643[gr-qc

  • [96]

    J. M. Toledo and V. B. Bezerra, Int. J. Mod. Phys. D 28, 1950023 (2019)

  • [97]

    M. F. A. R. Sakti, H. L. Prihadi, A. Suroso et al., in Journal of Physics Conference Series, Journal of Physics Conference Series, Vol. 1949 (2021) p. 012016

  • [98]

    E. Herscovich and M. G. Richarte, Phys. Lett. B 689, 192 (2010), arXiv:1004.3754[hep-th

  • [99]

    A. Vilenkin and E. P. S. Shellard, (2000)

  • [100]

    M. Barriola and A. Vilenkin, Phys. Rev. Lett. 63, 341 (1989)

  • [101]

    P. S. Letelier, Phys. Rev. D 20, 1294 (1979)

  • [102]

    S. Tsujikawa, Class. and Quantum Gra. 30, 214003 (2013), arXiv:1304.1961[gr-qc

  • [103]

    A. Liaqat and I. Hussain, Chin. Phys. C 46, 015101 (2022)

  • [104]

    W. Miranda, S. Carneiro, and C. Pigozzo, JCAP 2014, 043 (2014), arXiv:1405.3673[astro-ph.CO

  • [105]

    V. Perlick and O. Y. Tsupko, Phys. Rep. 947, 1 (2022), arXiv:2105.07101[gr-qc

  • [106]

    U. Papnoi and F. Atamurotov, Physics of the Dark Universe 35, 100916 (2022), arXiv:2111.15523[gr-qc

  • [107]

    K. Jusufi, M. Jamil, and T. Zhu, Eur. Phys. J. C 80, 354 (2020), arXiv:2005.05299[gr-qc

  • [108]

    K. Akiyama and, et al., Astrophys. J. Lett 930, L12 (2022)

  • [109]

    M. Sharif and S. Iftikhar, Adv. High Energy Phys. 2015, 635625 (2015), [Erratum: Adv.High Energy Phys. 2015, 219762 (2015)]