[1] A. Einstein, Phys. Z. 15, 176 (1914).
[2] A. Einstein, j-S-B-Preuss. Akad. Wiss. 2, 1030 (1914).
[3] A. Einstein, j-S-B-Preuss. Akad. Wiss. 2, 778 (1915).
[4] A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1915, 831 (1915).
[5] A. Einstein, Ann. Phys. (Berlin) 354, 769 (1916).
[6] S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Cambridge University Press, Cambridge, England, 2004).
[7] C. M. Will, Living Rev. Relativity 9, 3 (2006).
[8] F. W. Dyson, A. S. Eddington, and C. Davidson, Phil. Trans. R. Soc. A 220, 291 (1920).
[9] B. P. Abbott et al. (LIGO Scientific and Virgo Collabora- tions), Phys. Rev. Lett. 116, 061102 (2016).
[10] M. De Laurentis, O. Porth, L. Bovard, B. Ahmedov, and A. Abdujabbarov, Phys. Rev. D 94, 124038 (2016).
[11] C. Corda, Int. J. Mod. Phys. D 18, 2275 (2009).
[12] H. Weyl, Ann. Phys. (Berlin) 364, 101 (1919).
[13] J. W. Dyson, Math. Gazette 12, 351 (1925).
[14] A. De Felice and S. Tsujikawa, Living Rev. Relativity 13,3 (2010).
[15] S. Capozziello and M. De Laurentis, Phys. Rep. 509, 167 (2011).
[16] S. Nojiri and S. D. Odintsov, Phys. Rep. 505, 59 (2011).
[17] A. M. Awad, S. Capozziello, and G. G. L. Nashed, J. High Energy Phys. 07 (2017) 136.
[18] G. G. L. Nashed and E. N. Saridakis, Classical Quant. Grav. 36, 135005 (2019).
[19] T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, Phys. Rev. D 84, 024020 (2011).
[20] M. Chaichian, J. Kluson, M. Oksanen, and A. Tureanu, J. High Energy Phys. 12 (2014) 102.
[21] A. H. Chamseddine, V. Mukhanov, and A. Vikman, J. Cosmol. Astropart. Phys. 06 (2014) 017.
[22] A. Golovnev, Phys. Lett. B 728, 39 (2014).
[23] D. Momeni, A. Altaibayeva, and R. Myrzakulov, Int. J. Geom. Methods Mod. Phys. 11, 1450091 (2014).
[24] N. Deruelle and J. Rua, J. Cosmol. Astropart. Phys. 09 (2014) 002.
[25] S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Rep. 692, 1 (2017).
[26] L. Sebastiani, S. Vagnozzi, and R. Myrzakulov, Adv. High Energy Phys. 2017, 3156915 (2017).
[27] S. Nojiri and S. D. Odintsov, Mod. Phys. Lett. A 29, 1450211 (2014).
[28] S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 93, 023517 (2016).
[29] S. D. Odintsov and V. K. Oikonomou, Astrophys. Space Sci. 361, 174 (2016).
[30] S. D. Odintsov and V. K. Oikonomou, Ann. Phys. (Amsterdam) 363, 503 (2015).
[31] G. Leon and E. N. Saridakis, J. Cosmol. Astropart. Phys. 04 (2015) 031.
[32] R. Myrzakulov and L. Sebastiani, Astrophys. Space Sci. 361, 188 (2016).
[33] D. Momeni, R. Myrzakulov, and E. Güdekli, Int. J. Geom. Methods Mod. Phys. 12, 1550101 (2015).
[34] A. V. Astashenok, S. D. Odintsov, and V. K. Oikonomou, Classical Quant. Grav. 32, 185007 (2015).
[35] R. Myrzakulov, L. Sebastiani, and S. Vagnozzi, Eur. Phys. J. C 75, 444 (2015).
[36] G. Cognola, R. Myrzakulov, L. Sebastiani, S. Vagnozzi, and S. Zerbini, Classical Quant. Grav. 33, 225014 (2016).
[37] F. Arroja, N. Bartolo, P. Karmakar, and S. Matarrese, J. Cosmol. Astropart. Phys. 09 (2015) 051.
[38] A. Ijjas, J. Ripley, and P. J. Steinhardt, Phys. Lett. B 760, 132 (2016).
[39] H. Saadi, Eur. Phys. J. C 76, 14 (2016).
[40] J. Matsumoto, S. D. Odintsov, and S. V. Sushkov, Phys. Rev. D 91, 064062 (2015).
[41] R. Myrzakulov, L. Sebastiani, S. Vagnozzi, and S. Zerbini, Fundam. J. Mod. Phys. 8, 119 (2015).
[42] Y. Rabochaya and S. Zerbini, Eur. Phys. J. C 76, 85 (2016).
[43] R. Myrzakulov, L. Sebastiani, S. Vagnozzi, and S. Zerbini, Classical Quant. Grav. 33, 125005 (2016).
[44] V. K. Oikonomou, Universe 2, 10 (2016).
[45] R. Myrzakulov and L. Sebastiani, Gen. Relativ. Gravit. 47, 89 (2015).
[46] V. K. Oikonomou, Int. J. Mod. Phys. 25, 1650078 (2016).
[47] A. V. Astashenok and S. D. Odintsov, Phys. Rev. D 94, 063008 (2016).
[48] G. Domenech, S. Mukohyama, R. Namba, A. Naruko, R. Saitou, and Y. Watanabe, Phys. Rev. D 92, 084027 (2015).
[49] H. Firouzjahi, M. A. Gorji, S. A. Hosseini Mansoori, A. Karami, and T. Rostami, J. Cosmol. Astropart. Phys. 11 (2018) 046.
[50] L. Shen, Y. Zheng, and M. Li, J. Cosmol. Astropart. Phys. 12 (2019) 026.
[51] M. A. Gorji, A. Allahyari, M. Khodadi, and H. Firouzjahi, Phys. Rev. D 101, 124060 (2020).
[52] A. Sheykhi, J. High Energy Phys. 01 (2021) 043.
[53] S. W. Hawking, M. J. Perry, and A. Strominger, Phys. Rev. Lett. 116, 231301 (2016).
[54] K. Akiyama et al. (Event Horizon Telescope Collabora- tion), Astrophys. J. 875, L1 (2019).
[55] H. Afshar, S. Detournay, D. Grumiller, W. Merbis, A. Perez, D. Tempo, and R. Troncoso, Phys. Rev. D 93, 101503 (2016).
[56] S. Haco, S. W. Hawking, M. J. Perry, and A. Strominger, J. High Energy Phys. 12 (2018) 098.
[57] W. El Hanafy and G. G. L. Nashed, Astrophys. Space Sci. 361, 68 (2016).
[58] S. Haco, M. J. Perry, and A. Strominger, arXiv: 1902.02247.
[59] G. G. L. Nashed, Nuovo Cimento Soc. Ital. Fis. 117B, 521 (2002).
[60] D. Grumiller, A. Pe´rez, M. M. Sheikh-Jabbari, R. Troncoso, and C. Zwikel, Phys. Rev. Lett. 124, 041601 (2020).
[61] W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).
[62] J. Schwinger, Phys. Rev. 82, 664 (1951).
[63] R. Ruffini, Y.-B. Wu, and S.-S. Xue, Phys. Rev. D 88, 085004 (2013).
[64] R. Ruffini, G. Vereshchagin, and S.-S. Xue, Phys. Rep. 487, 1 (2010).
[65] K. A. Bronnikov, Phys. Rev. D 63, 044005 (2001).
[66] K. Bronnikov, V. Melnikov, G. Shikin, and K. Staniukovich, Ann. Phys. (N.Y.) 118, 84 (1979).
[67] A. Awad and G. Nashed, J. Cosmol. Astropart. Phys. 02 (2017) 046.
[68] H. Yajima and T. Tamaki, Phys. Rev. D 63, 064007 (2001).
[69] I. Z. Stefanov, S. S. Yazadjiev, and M. D. Todorov, Mod. Phys. Lett. A 22, 1217 (2007).
[70] A. Allahyari, M. Khodadi, S. Vagnozzi, and D. F. Mota, J. Cosmol. Astropart. Phys. 02 (2020) 003.
[71] G. G. L. Nashed, Mod. Phys. Lett. A 22, 1047 (2007).
[72] C. Corda and H. J. Mosquera Cuesta, Mod. Phys. Lett. A 25, 2423 (2010).
[73] S. H. Hendi and M. Allahverdizadeh, Adv. High Energy Phys. 2014, 390101 (2014).
[74] N. Breton and L. A. Lopez, Phys. Rev. D 94, 104008 (2016).
[75] M. Maceda and A. Macías, Phys. Lett. B 788, 446 (2019).
[76] J. C. Olvera and L. A. López, Eur. Phys. J. Plus 135, 288 (2020).
[77] E. A. Lim, I. Sawicki, and A. Vikman, J. Cosmol. Astropart. Phys. 05 (2010) 012.
[78] C. Gao, Y. Gong, X. Wang, and X. Chen, Phys. Lett. B 702, 107 (2011).
[79] S. Capozziello, J. Matsumoto, S. Nojiri, and S. D. Odintsov, Phys. Lett. B 693, 198 (2010).
[80] A. H. Chamseddine and V. Mukhanov, J. High Energy Phys. 11 (2013) 135.
[81] S. W. Hawking and G. E. R. Ellis, The Large Scale Structure of Spacetime (Cambridge University Press, Cambridge, England, 1973).
[82] G. G. L. Nashed, Adv. High Energy Phys. 2016, 7020162 (2016).
[83] S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Lett. B 775, 44 (2017).
[84] A. Sheykhi, Phys. Rev. D 86, 024013 (2012).
[85] A. Sheykhi, Eur. Phys. J. C 69, 265 (2010).
[86] S. H. Hendi, A. Sheykhi, and M. H. Dehghani, Eur. Phys. J. C 70, 703 (2010).
[87] A. Sheykhi, M. H. Dehghani, and S. H. Hendi, Phys. Rev. D 81, 084040 (2010).
[88] G. Cognola, O. Gorbunova, L. Sebastiani, and S. Zerbini, Phys. Rev. D 84, 023515 (2011).
[89] Y. Zheng and R.-J. Yang, Eur. Phys. J. C 78, 682 (2018).
[90] P. C. W. Davies, Proc. R. Soc. A 353, 499 (1977).
[91] G. G. L. Nashed, Chaos Solitons Fractals 15, 841 (2003).
[92] Y. S. Myung, Phys. Rev. D 84, 024048 (2011).
[93] Y. S. Myung, Phys. Rev. D 88, 104017 (2013).
[94] K. Nouicer, Classical Quant. Grav. 24, 5917 (2007); 24, 6435(E) (2007).
[95] I. Dymnikova and M. Korpusik, Entropy 13, 1967 (2011).
[96] A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, Phys. Rev. D 60, 064018 (1999).
[97] Y. Zheng and R. Yang, Eur. Phys. J. C 78, 682 (2018).
[98] O. Ökcü and E. Aydıner, Eur. Phys. J. C 78, 123 (2018).
[99] R. A. D’Inverno, Internationale Elektronische Rundschau (Oxford University press, Oxford, 1992).
[100] H. A. Buchdahl, Phys. Rev. 115, 1325 (1959).
[101] D. Momeni, K. Myrzakulov, R. Myrzakulov, and M. Raza, Eur. Phys. J. C 76, 301 (2016).