Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity

  • We analyze the four common types of finite-time singularity using a generic framework of the phase portrait geometric approach. This technique requires the Friedmann system to be written as a one-dimensional autonomous system. We employ a scale factor that has been used widely in the literature to realize the four finite-time singularity types, then we give a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f(T) cosmology is compatible with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f(T) theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.
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  • [1] Shin'ichi Nojiri and Sergei D. Odintsov, Phys. Lett. B, 595:1-8 (2004), arXiv:hep-th/0405078[hep-th]
    [2] Petr Tretyakov, Aleksey Toporensky, Yuri Shtanov, and Varun Sahni, Class. Quant. Grav., 23:3259-3274 (2006), arXiv:gr-qc/0510104[gr-qc]
    [3] John D. Barrow, Antonio B. Batista, Julio C. Fabris, Mahouton J. S. Houndjo, and Giuseppe Dito, Phys. Rev. D, 84:123518 (2011), arXiv:1110.1321[gr-qc]
    [4] Zoltan Keresztes, Laszlo A. Gergely, and Alexander Yu. Kamenshchik, Phys. Rev. D, 86:063522 (2012), arXiv:1204.1199[gr-qc]
    [5] John D. Barrow and S. Cotsakis, Phys. Rev. D, 88:067301 (2013), arXiv:1307.5005[gr-qc]
    [6] A. Yu. Kamenshchik, E. O. Pozdeeva, Sergey Yu. Vernov, A. Tronconi, and G. Venturi, Phys. Rev. D, 94:063510 (2016), arXiv:1602.07192[gr-qc]
    [7] A. Awad and G. Nashed, J. Cosm. Astropart. Phys., 2:046 (2017), arXiv:1701.06899[gr-qc]
    [8] Mariusz P. Dabrowski, Tomasz Denkiewicz, and Martin A. Hendry, Phys. Rev. D, 75:123524 (2007), arXiv:0704.1383[astro-ph]
    [9] Z. Keresztes, L. A. Gergely, V. Gorini, U. Moschella, and A. Yu. Kamenshchik, Phys. Rev. D, 79:083504 (2009), arXiv:0901.2292[gr-qc]
    [10] K. Kleidis and V. K. Oikonomou, Astrophys. Space Sci., 361:326 (2016), arXiv:1609.00848[gr-qc]
    [11] Jerome Martin and Robert H. Brandenberger, Phys. Rev., 123501 (2001), arXiv:hep-th/0005209[hep-th]
    [12] Robert H. Brandenberger and Jerome Martin, Class. Quant. Grav., 30:113001 (2013), arXiv:1211.6753[astro-ph.CO]
    [13] David Wands, Phys. Rev., 023507 (1999), arXiv:grqc/9809062[gr-qc]
    [14] Fabio Finelli and Robert Brandenberger, Phys. Rev., 103522 (2002), arXiv:hep-th/0112249[hep-th]
    [15] Tirthabir Biswas, Riley Mayes, and Colleen Lattyak, Phys. Rev., 063505 (2016), arXiv:1502.05875[gr-qc]
    [16] M. Novello and S. E. Perez Bergliaffa, Phys. Rept., 463:127-213 (2008), arXiv:0802.1634[astro-ph]
    [17] Yi-Fu Cai, Sci. China Phys. Mech. Astron., 57:1414-1430 (2014), arXiv:1405.1369[hep-th]
    [18] D. Battefeld and Patrick Peter, Phys. Rept., 571:1-66 (2015), arXiv:1406.2790[astro-ph.CO]
    [19] Robert Brandenberger and Patrick Peter, Found. Phys., 47:797-850 (2017), arXiv:1603.05834[hep-th]
    [20] Y.-F. Cai, S.-H. Chen, J. B. Dent, S. Dutta, and E. N. Saridakis, Classical and Quantum Gravity, 28:215011 (2011), arXiv:1104.4349[astro-ph]
    [21] Jaume Amors, Jaume de Haro, and Sergei D. Odintsov, Phys. Rev. D, 87:104037 (2013), arXiv:1305.2344[gr-qc]
    [22] S. D. Odintsov and V. K. Oikonomou, Int. J. Mod. Phys., 1750085 (2017), arXiv:1512.04787[gr-qc]
    [23] Kazuharu Bamba, G. G. L. Nashed, W. El Hanafy, and S.K. Ibraheem, Phys. Rev. D, 94:(2016), 10.1103/PhysRevD.94.083513, arXiv:1604.07604[gr-qc]
    [24] W. El Hanafy and G. G. L. Nashed, Int. J. Mod. Phys., 1750154 (2017), arXiv:1707.01802[gr-qc]
    [25] Shin'ichi Nojiri, Sergei D. Odintsov, and Shinji Tsujikawa, Phys. Rev. D, 71:063004 (2005), arXiv:hep-th/0501025[hepth]
    [26] Shin'ichi Nojiri and Sergei D. Odintsov, Phys. Rev. D, 78:046006 (2008), arXiv:0804.3519[hep-th]
    [27] John D. Barrow, Class. Quant. Grav., 21:L79-L82 (2004), arXiv:gr-qc/0403084[gr-qc]
    [28] John D. Barrow, Class. Quant. Grav., 21:5619-5622 (2004), arXiv:gr-qc/0409062[gr-qc]
    [29] S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D, 92:124024 (2015), arXiv:1510.04333[gr-qc]
    [30] S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D, 92:024058 (2015), arXiv:1507.05273[gr-qc]
    [31] I. Brevik, V. V. Obukhov, and A. V. Timoshkin, Mod. Phys. Lett. A, 31:1650105 (2016), arXiv:1604.04748[gr-qc]
    [32] A. Awad, Phys. Rev. D, 87:103001 (2013),[Erratum:Phys. Rev.D87,no.10,109902(2013)], arXiv:1303.2014[gr-qc]
    [33] A. Awad, W. El Hanafy, G. G. L. Nashed, and E. N. Saridakis, (2017), arXiv:1710.10194
    [34] Steven H. Strogatz, Nonlinear Dynamics And Chaos:With Applications To Physics, Biology, Chemistry And Engineering, Studies in Nonlinearity, Vol. 1 (1994)
    [35] S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D, 92:024016 (2015), arXiv:1504.06866[gr-qc]
    [36] Omer Farooq, Foram Ranjeet Madiyar, Sara Crandall, and Bharat Ratra, (2016), arXiv:1607.03537[astro-ph.CO]
    [37] S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Lett. B, 747:310-320 (2015), arXiv:1506.03307[gr-qc]
    [38] J. W. Maluf, Ann. Phys. (Berlin), 525:339-357 (2013), arXiv:1303.3897[gr-qc]
    [39] G. Kofinas and E.N. Saridakis, Phys. Rev. D, 90:084044 (2014), arXiv:1404.2249[gr-qc]
    [40] Salvatore Capozziello, Mariafelicia De Laurentis, and Konstantinos F. Dialektopoulos, Eur. Phys. J. C, 76, 629 (2016), arXiv:1609.09289[gr-qc]
    [41] Martin Krk and J. G. Pereira, Eur. Phys. J. C, 75:519 (2015), arXiv:1504.07683[gr-qc]
    [42] M. Krk and E. N. Saridakis, Classical and Quantum Gravity, 33:115009 (2016), arXiv:1510.08432[gr-qc]
    [43] F. I. Mikhail and M. I. Wanas, Proc. Roy. Soc. London Ser. A,, 356:471-481 (1977)
    [44] F. I. Mikhail and M. I. Wanas, Int. J. Theoret. Phys., 20:671-680 (1981)
    [45] M. I. Wanas, Int. J. Theoret. Phys., 24, 6:639-651 (1985)
    [46] M. I. Wanas, Astrophys. Space Sci., 127:21-25 (1986)
    [47] M. I. Wanas, Astrophys. Space Sci., 258:237-248 (1998), arXiv:9904019[gr-qc]
    [48] F. I. Mikhail, M. I. Wanas, and A. M. Eid, Astrophys. Space Sci., 228:221-237 (1995)
    [49] M. I. Wanas and M. E. Kahil, Gen. Rel. Grav., 31:1921 (1999), arXiv:gr-qc/9912007[gr-qc]
    [50] Nabil L. Youssef and Amr M. Sid-Ahmed, Rep. Math. Phys,, 60:39-53 (2007), arXiv:0604111[gr-qc]
    [51] Nabil L. Youssef and Amr M. Sid-Ahmed, Int. J. Geom. Meth. Mod. Phys., 5:1109-1135 (2008), arXiv:0805.1336[math.DG]
    [52] Nabil L. Youssef and Waleed A. Elsayed, Rep. Math. Phys., 72:1-23 (2013), arXiv:1209.1379[gr-qc]
    [53] M. I. Wanas, Turkish J. Phys., 24:473-488 (2000), arXiv:0010099[gr-qc]
    [54] M. I. Wanas, Stud. Cercet. Stiin. Ser. Mat., 10:297-309 (2001), arXiv:0209050[gr-qc]
    [55] M. I. Wanas, M. Melek, and M. E. Kahil, Gravit. Cosmol., 6:319-322 (2000), arXiv:9812085[gr-qc]
    [56] M. I. Wanas, M. Melek, and M. E. Kahil, in Galaxies and their constituents at the highest angular resolutions, IAU Symposium, Vol. 205:edited by R. T. Schilizzi (2001, p. 396) arXiv:0306086[gr-qc]
    [57] M. I. Wanas, Int. J. Geom. Meth. Mod. Phys., 4:373-388 (2007), arXiv:0703036[gr-qc]
    [58] M. I. Wanas, Adv. High Energy Phys., 2012:Article ID 752613, 10 pages (2012)
    [59] M. I. Wanas and S. A. Ammar, Mod. Phys. Lett. A, 25, 1705-1721 (2010), arXiv:0505092[gr-qc]
    [60] M.I. Wanas, N.L. Youssef, W. El Hanafy, and S.N. Osman, Adv. Math. Phys., 2016 (2016), 10.1155/2016/1037849 arXiv:1611.06075[gr-qc]
    [61] M. I. Wanas, Nabil L. Youssef, and W. El Hanafy, Grav. Cosmol., 23:105-118 (2017), arXiv:1404.2485[gr-qc]
    [62] B. Li, T. P. Sotiriou, and J. D. Barrow, Phys. Rev. D, 83:064035 (2011), arXiv:1010.1041[gr-qc]
    [63] T. P. Sotiriou, B. Li, and J. D. Barrow, Phys. Rev. D, 83:104030 (2011), arXiv:1012.4039[gr-qc]
    [64] R. Ferraro and F. Fiorini, Phys. Rev. D, 91:064019 (2015), arXiv:1412.3424[gr-qc]
    [65] G. G. L. Nashed, Chin. Phys., 020401 (2010), arXiv:0910.5124[gr-qc]
    [66] G. R. Bengochea and R. Ferraro, Phys. Rev. D, 79:124019 (2009), arXiv:0812.1205[astro-ph]
    [67] E. V. Linder, Phys. Rev. D, 81:127301 (2010), arXiv:1005.3039[astro-ph]
    [68] S. Capozziello, V. F. Cardone, H. Farajollahi, and A. Ravanpak, Phys. Rev. D, 84:043527 (2011), arXiv:1108.2789[astro-ph]
    [69] Salvatore Capozziello, Orlando Luongo, and Emmanuel N. Saridakis, Phys. Rev. D, 91:124037 (2015), arXiv:1503.02832[gr-qc]
    [70] K. Bamba and C.-Q. Geng, J. Cosmol. Astropart. Phys., 11:008 (2011), arXiv:1109.1694[gr-qc]
    [71] H. Mohseni Sadjadi, Physics Letters B, 718:270-275 (2012), arXiv:1210.0937[gr-qc]
    [72] K. Bamba, R. Myrzakulov, S. Nojiri, and S. D. Odintsov, Phys. Rev. D, 85:104036 (2012), arXiv:1202.4057[gr-qc]
    [73] K. Bamba, S. Capozziello, M. De Laurentis, S. Nojiri, and D. Sez-Gmez, Phys. Lett. B, 727:194-198 (2013), arXiv:1309.2698[gr-qc]
    [74] K. Bamba, C.-Q. Geng, C.-C. Lee, and L.-W. Luo, J. Cosmol. Astropart. Phys. 1:021 (2011), arXiv:1011.0508[astroph]
    [75] G.G. L. Nashed and W. El Hanafy, Eur. Phys. J. C, 74:(2014), 10.1140/epjc/s10052-014-3099-5 arXiv:1403.0913[grqc]
    [76] G. G. L. Nashed, Gen. Relativ. Gravit., 47:75 (2015), arXiv:1506.08695[gr-qc]
    [77] W. El Hanafy and G. G. L. Nashed, Eur. Phys. J. C, 75 (2015), 10.1140/epjc/s10052-015-3501-y arXiv:1409.7199[hep-th]
    [78] W. El Hanafy and G. G. L. Nashed, Astrophys. Space Sci., 361 (2016), 10.1007/s10509-016-2853-6 arXiv:1510.02337[grqc]
    [79] W. El Hanafy and G. G. L. Nashed, Astrophys. Space Sci., 361 (2016), 10.1007/s10509-016-2786-0 arXiv:1410.2467[hepth]
    [80] Lorenzo Iorio, Ninfa Radicella, and Matteo Luca Ruggiero, J. Cosmol. Astropart. Phys., 1508:021 (2015), arXiv:1505.06996[gr-qc]
    [81] W. El Hanafy and G. G. L. Nashed, Astrophys. Space Sci., 361 (2016), 10.1007/s10509-016-2662-y arXiv:1507.07377[grqc]
    [82] Andrew DeBenedictis and Sasa Ilijic, Phys. Rev. D, 94:124025 (2016), arXiv:1609.07465[gr-qc]
    [83] Gabriel Farrugia, Jackson Levi Said, and Matteo Luca Ruggiero, Phys. Rev. D, 93:104034 (2016), arXiv:1605.07614[gr-qc]
    [84] Ednaldo L. B. Junior, Manuel E. Rodrigues, and Mahouton J. S. Houndjo, J. Cosmol. Astropart. Phys. 1510:060 (2015), arXiv:1503.07857[gr-qc]
    [85] Salvatore Capozziello, P. A. Gonzalez, Emmanuel N. Saridakis, and Yerko Vasquez, JHEP, 02:039 (2013), arXiv:1210.1098[hep-th]
    [86] G. G. L Nashed and W. El Hanafy, Eur. Phys. J. C, 77:90 (2017), arXiv:1612.05106[gr-qc]
    [87] G. G. L. Nashed, Chaos Solitons Fractals, 15:841 (2003), arXiv:gr-qc/0301008[gr-qc]
    [88] G. G. L. Nashed, Phys. Rev., 104034 (2013), arXiv:1311.3131[gr-qc]
    [89] G. G. L. Nashed, Gen. Rel. Grav., 45:1887-1899 (2013), arXiv:1502.05219[gr-qc]
    [90] G. G. L. Nashed, Chinese Physics Letters, 29:050402 (2012), arXiv:1111.0003[physics.gen-ph]
    [91] Yi-Fu Cai, Salvatore Capozziello, Mariafelicia De Laurentis, and Emmanuel N. Saridakis, Rept. Prog. Phys., 79:106901 (2016), arXiv:1511.07586[gr-qc]
    [92] Jun-Qing Xia, Yi-Fu Cai, Tao-Tao Qiu, Gong-Bo Zhao, and Xinmin Zhang, Int. J. Mod. Phys., 1229-1243 (2008), arXiv:astro-ph/0703202[astro-ph]
    [93] Yi-Fu Cai, Emmanuel N. Saridakis, Mohammad R. Setare, and Jun-Qing Xia, Phys. Rept., 493:1-60 (2010), arXiv:0909.2776[hep-th]
    [94] Bo Feng, Xiu-Lian Wang, and Xin-Min Zhang, Phys. Lett., 35-41 (2005), arXiv:astro-ph/0404224[astro-ph]
    [95] Zong-Kuan Guo, Yun-Song Piao, Xin-Min Zhang, and YuanZhong Zhang, Phys. Lett., 177-182 (2005), arXiv:astroph/0410654[astro-ph]
    [96] Irina Ya. Aref'eva, A. S. Koshelev, and S. Yu. Vernov, Phys. Rev., 064017 (2005), arXiv:astro-ph/0507067[astro-ph]
    [97] Ming-zhe Li, Bo Feng, and Xin-min Zhang, JCAP, 0512:002 (2005), arXiv:hep-ph/0503268[hep-ph]
    [98] I. Ya. Aref'eva and A. S. Koshelev, JHEP, 02:041 (2007), arXiv:hep-th/0605085[hep-th]
    [99] S.-H. Chen, J. B. Dent, S. Dutta, and E. N. Saridakis, Phys. Rev. D, 83:023508 (2011), arXiv:1008.1250[astro-ph]
    [100] K. Rezazadeh, A. Abdolmaleki, and K. Karami, J. High Energy Phys., 01:131 (2016), arXiv:1509.08769[gr-qc]
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El Hanafy and G. G. L. Nashed. Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity[J]. Chinese Physics C, 2017, 41(12): 125103. doi: 10.1088/1674-1137/41/12/125103
El Hanafy and G. G. L. Nashed. Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity[J]. Chinese Physics C, 2017, 41(12): 125103.  doi: 10.1088/1674-1137/41/12/125103 shu
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Received: 2017-08-16
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    Supported by the Egyptian Ministry of Scientific Research (24-2-12)

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Generic phase portrait analysis of finite-time singularities and generalized teleparallel gravity

    Corresponding author: El Hanafy,
    Corresponding author: G. G. L. Nashed,
  • 1. Centre for Theoretical Physics, The British University in Egypt, P. O. Box 43, El Sherouk City, Cairo 11837, Egypt
  • 2. Egyptian Relativity Group(ERG), Cairo University, Giza 12613, Egypt
  • 3. Mathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt
  • 4. Egyptian Relativity Group(ERG), Cairo University, Giza 12613, Egypt
Fund Project:  Supported by the Egyptian Ministry of Scientific Research (24-2-12)

Abstract: We analyze the four common types of finite-time singularity using a generic framework of the phase portrait geometric approach. This technique requires the Friedmann system to be written as a one-dimensional autonomous system. We employ a scale factor that has been used widely in the literature to realize the four finite-time singularity types, then we give a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f(T) cosmology is compatible with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f(T) theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.

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