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

El Hanafy; G. G. L. Nashed

doi:10.1088/1674-1137/41/12/125103

Chinese Physics C> 2017, Vol. 41> Issue(12) : 125103 DOI: 10.1088/1674-1137/41/12/125103

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

El Hanafy ^1,3,, ,
G. G. L. Nashed ^1,2,3,,

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

Abstract
HTML
Reference
Related

PDF

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.
- inflation ,
- bounce ,
- big brake ,
- CDM ,
- teleparallel gravity

References

[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]

[1]	M. Shahalam . Evolution of the universe prior to inflation in loop quantum cosmology. Chinese Physics C, 2025, 49(4): 1-8.
[2]	Wei Cheng , Tong Qin , Jiujiang Jiang , Ruiyu Zhou . Constraints on real scalar inflation from preheating using LATTICEEASY. Chinese Physics C, 2024, 48(6): 065108. doi: 10.1088/1674-1137/ad34bd
[3]	Haipeng An , Kun-Feng Lyu , Lian-Tao Wang , Siyi Zhou . A unique gravitational wave signal from phase transition during inflation. Chinese Physics C, 2022, 46(10): 101001. doi: 10.1088/1674-1137/ac76a7
[4]	Mingzhe Li , Yicen Mou , Haomin Rao , Dehao Zhao . Gravitational leptogenesis in teleparallel and symmetric teleparallel gravities. Chinese Physics C, 2022, 46(2): 025101. doi: 10.1088/1674-1137/ac3411
[5]	Bao-Min Gu , Robert Brandenberger . Reheating and entropy perturbations in fibre inflation. Chinese Physics C, 2020, 44(1): 015103. doi: 10.1088/1674-1137/44/1/015103
[6]	Nan Zhang , Ya-Bo Wu , Jun-Wang Lu , Chu-Wen Sun , Li-Jie Shou , Hai-Zhou Xu . Constraints on the generalized natural inflation after Planck 2018. Chinese Physics C, 2020, 44(9): 095107. doi: 10.1088/1674-1137/44/9/095107
[7]	Andrea Addazi , Stephon Alexander , Yi-Fu Cai , Antonino Marcianó . Dark matter and baryogenesis in the Fermi-bounce curvaton mechanism. Chinese Physics C, 2018, 42(6): 065101. doi: 10.1088/1674-1137/42/6/065101
[8]	Hai-Nan Lin , Xin Li , Yu Sang . Local probes strongly favor ∧CDM against power-law and R_h=ct universe. Chinese Physics C, 2018, 42(9): 095101. doi: 10.1088/1674-1137/42/9/095101
[9]	Xian Gao , Lavinia Heisenberg . Doubly coupled matter fields in massive bigravity. Chinese Physics C, 2018, 42(7): 075101. doi: 10.1088/1674-1137/42/7/075101
[10]	Jun Chen , Wenjie Hou , Taotao Qiu , Defu Hou . Comparing potential-driven DBI-inspired non-minimal kinetic coupling (Dinkic) inflation with observational data. Chinese Physics C, 2018, 42(4): 045102. doi: 10.1088/1674-1137/42/4/045102
[11]	Ata Sojasi , Ebrahim Yusofi , Majid Mohsenzadeh . Asymptotic-de sitter inflation in the light of the planck data. Chinese Physics C, 2018, 42(11): 115102. doi: 10.1088/1674-1137/42/11/115102
[12]	Jinn-Ouk Gong , Seong Chan Park . A minimal gauge inflation model. Chinese Physics C, 2018, 42(9): 095102. doi: 10.1088/1674-1137/42/9/095102
[13]	M. Mohsenzadeh , E. Yusofi . Higher order corrections to asymptotic-de Sitter inflation. Chinese Physics C, 2017, 41(8): 085101. doi: 10.1088/1674-1137/41/8/085101
[14]	Yacine Bouguerra , Mustapha Maamache , Jeong Ryeol Choi . Nonlinear description of Yang-Mills cosmology: cosmic inflation and the accompanying Hannay's angle. Chinese Physics C, 2017, 41(6): 065103. doi: 10.1088/1674-1137/41/6/065103
[15]	Fa-Peng Huang , Yifu Cai , Hong Li , Xinmin Zhang . A possible interpretation of the Higgs mass by the cosmological attractive relaxion. Chinese Physics C, 2016, 40(11): 113103. doi: 10.1088/1674-1137/40/11/113103
[16]	ZHAO Dong , LI Ming-Hua , WANG Ping , CHANG Zhe . Inflation in de Sitter spacetime and CMB large scale anomaly. Chinese Physics C, 2015, 39(9): 095101. doi: 10.1088/1674-1137/39/9/095101
[17]	FAN Guang-Wei , CAI Xiao-Lu , HAN Ti-Fei , LI Xue-Chao , REN Zhong-Zhou , XU Wang . Big deformation in ¹⁷C. Chinese Physics C, 2014, 38(1): 014101. doi: 10.1088/1674-1137/38/1/014101
[18]	CHANG Zhe , LI Ming-Hua , LI Xin . Constraints from Type Ia supernovae on the Λ-CDM model in Randers-Finsler space. Chinese Physics C, 2012, 36(8): 710-715. doi: 10.1088/1674-1137/36/8/005
[19]	XU Jian-Jun , LI Xin-Zhou , NI Guang-Jiong . AN INFLATION SOLUTION FROM THE CALABI-YAU COMPACTIFICATION. Chinese Physics C, 1988, 12(6): 852-856.
[20]	Xu Jianjun , Li Xinzhou , Ni Guangjiong . An Inflation Solution from the Calabi-Yau Compactification. Chinese Physics C, 1988, 12(S4): 393-398.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2017-08-16

Fund

Supported by the Egyptian Ministry of Scientific Research (24-2-12)

Article Metric

Article Views(1589)
PDF Downloads(95)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

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

Corresponding author: El Hanafy,

Corresponding author: G. G. L. Nashed,

HTML

目录