Cosmological study of autonomous dynamical systems in modified Tele-Parallel gravity
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Abstract.
Cosmological approaches of an autonomous dynamical system studied in the framework of f(T) gravity are investigated in this paper. Our methods applied to flat Friedmann-Robertson-Walker equations in f(T) gravity, consisting in extracting dynamical systems whose time-dependence is contained in a single parameter m depending on the Hubble rate of the Universe and its second derivative order. In our attempt to investigate the autonomous aspect of the dynamical systems reconstructed in both vacuum and non-vacuum f (T) gravities, two constant values of the parameter m have been at the heart of our present analysis. In the so-called quasi-de Sitter inflationary era (\( m\simeq 0\)), the corresponding autonomous dynamical systems provide stable de Sitter attractors and unstable de Sitter fixed points. Especially in vacuum f(T) gravity, the approximate form of the f(T) gravities near the stable and the unstable de Sitter fixed points has been performed. The matter dominated era case \( (m=-\frac{9}{2})\) leads to unstable fixed points confirming matter dominated era or not, and stable attractor fixed point describing dark energy dominated era. Another subtlety around the stable fixed point obtained at the matter dominated case in the non-vacuum f(T) gravity is that when the dark energy dominated era is reached, at the same time, the radiation perfect fluid dominated succumbs.
References
- 1.A.A. Starobinsky, Phys. Lett. B 91, 99 (1980)ADSCrossRefGoogle Scholar
- 2.K. Sato, Mon. Not. R. Astron. Soc. 195, 467 (1981)ADSCrossRefGoogle Scholar
- 3.A.H. Guth, Phys. Rev. D 23, 347 (1981)ADSCrossRefGoogle Scholar
- 4.A.D. Linde, Phys. Lett. B 108, 389 (1982)ADSCrossRefGoogle Scholar
- 5.A. Albrecht, P.J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)ADSCrossRefGoogle Scholar
- 6.D.N. Spergel et al., Astrophys. J. Suppl. 170, 377 (2007) arXiv:astro-ph/0603449ADSCrossRefGoogle Scholar
- 7.Supernova Cosmology Project Collaboration (S. Perlmutter et al.), Astrophys. J. 517, 565 (1999) astro-ph/9812133CrossRefGoogle Scholar
- 8.Supernova Search Team Collaboration (A.G. Riess et al.), Astron. J. 116, 1009 (1998) astro-ph/9805201CrossRefGoogle Scholar
- 9.SDSS Collaboration (M. Tegmark et al.), Phys. Rev. D 69, 103501 (2004) astro-ph/0310723CrossRefGoogle Scholar
- 10.SDSS Collaboration (U. Seljak et al.), Phys. Rev. D 71, 103515 (2005) astro-ph/0407372ADSCrossRefGoogle Scholar
- 11.SDSS Collaboration (D.J. Eisenstein et al.), Astrophys. J. 633, 560 (2005) astro-ph/0501171CrossRefGoogle Scholar
- 12.B. Jain, A. Taylor, Phys. Rev. Lett. 91, 141302 (2003) astro-ph/0306046ADSCrossRefGoogle Scholar
- 13.J.K. Adelman-McCarthy et al., Astrophys. J. Suppl. 175, 297 (2008) arXiv:0707.3413 [astro-ph]ADSCrossRefGoogle Scholar
- 14.R. Aldrovandi, J.G. Pereira, An Introduction to Teleparallel Gravity, https://doi.org/www.ift.unesp.br/users/jpereira/tele.pdf
- 15.K. Kleidis, V.K. Oikonomou, Int. Geom. Methods Mod. Phys. 15, 1850137 (2018) arXiv:1803.10748 [gr-qc]MathSciNetCrossRefGoogle Scholar
- 16.A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010) arXiv:1002.4928 [gr-qc]ADSCrossRefGoogle Scholar
- 17.K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, Astrophys. Space Sci. 342, 155 (2012) arXiv:1205.3421 [gr-qc]ADSCrossRefGoogle Scholar
- 18.S. Nojiri, S.D. Odintsov, ECONF C 0602061, 06 (2006)Google Scholar
- 19.S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007) arXiv:hep-th/0601213MathSciNetCrossRefGoogle Scholar
- 20.S. Nojiri, S.D. Odintsov, V.K. Oikonomou, Phys. Rep. 692, 1 (2017)ADSMathSciNetCrossRefGoogle Scholar
- 21.F.G. Alvarenga, M.J.S. Houndjo, A.V. Monwanou, Jean. B. Chabi-Orou, arXiv:1205.4678 [gr-qc]Google Scholar
- 22.S. Nojiri, S.D. Odintsov, Phys. Lett. B 631, 1 (2005) hep-th/0508049ADSMathSciNetCrossRefGoogle Scholar
- 23.S. Nojiri, S.D. Odintsov, A. Toporensky, P. Tretyakov, arXiv:0912.2488Google Scholar
- 24.M.J.S. Houndjo, M.E. Rodrigues, D. Momeni, R. Myrzakulov, arXiv:1301.4642 [gr-qc]Google Scholar
- 25.E. Novikov, Mod. Phys. Lett. A 31, 1650092 (2016)ADSCrossRefGoogle Scholar
- 26.E. Novikov, Electron. J. Theor. Phys. 13, 79 (2016)Google Scholar
- 27.E. Novikov, Am. Res. J. Phys. 4, 1 (2018)Google Scholar
- 28.F. Hehl, P. Von Der Heyde, G. Kerclok, J. Nester, Rev. Mod. Phys. 48, 393 (1976)ADSCrossRefGoogle Scholar
- 29.J. Amorós, J. de Haro, S.D. Odintsov, Phys. Rev. D 87, 104037 (2013) arXiv:1305.2344 [gr-qc]ADSCrossRefGoogle Scholar
- 30.K. Bamba, J. de Haro, S.D. Odintsov, JCAP 1302, 008 (2013) arXiv:1211.2968 [gr-qc]ADSCrossRefGoogle Scholar
- 31.K. Bamba, S. ’i. Nojiri, S.D. Odintsov, arXiv:1304.6191 [gr-qc]Google Scholar
- 32.G.R. Bengochea, R. Ferraro, Phys. Rev. D 79, 124019 (2009) arXiv:0812.1205 [astro-ph]ADSCrossRefGoogle Scholar
- 33.E.V. Linder, Phys. Rev. D 81, 127301 (2010) 82ADSCrossRefGoogle Scholar
- 34.M.E. Rodrigues, I.G. Salako, M.J.S. Houndjo, J. Tossa, Int. J. Mod. Phys. D 23, 1450004 (2014)ADSCrossRefGoogle Scholar
- 35.Yi-Fu Cai, Salvatore Capozziello, Mariafelicia De Laurentis, Emmanuel N. Saridakis, arXiv:1511.07586v2 [gr-qc]Google Scholar
- 36.Manuel Hohmann, Laur Järv, Ulbossyn Ualikhanova, arXiv:1801.05786v2 [gr-qc]Google Scholar
- 37.Rafael C. Nunes, arXiv:1802.02281v2 [gr-qc]Google Scholar
- 38.Rafael C. Nunes, Supriya Pan, Emmanuel N. Saridakis, arXiv:1606.04359v2 [gr-qc]Google Scholar
- 39.M.M. Ivanov, A.V. Toporensky, Gravit. Cosmol. 18, 43 (2012) arXiv:1106.5179 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
- 40.S. Rippl, H. van Elst, R.K. Tavakol, D. Taylor, Gen. Relativ. Gravit. 28, 193 (1996) gr-qc/9511010ADSCrossRefGoogle Scholar
- 41.M. Khurshudyan, Int. J. Geom. Methods Mod. Phys. 14, 1750041 (2016)MathSciNetCrossRefGoogle Scholar
- 42.R.D. Boko, M.J.S. Houndjo, J. Tossa, Int. J. Mod. Phys. D 25, 1650098 (2016) arXiv:1605.03404 [gr-qc]ADSCrossRefGoogle Scholar
- 43.K. Kleidis, V.K. Oikonomou, arXiv:1808.04674 [gr-qc]Google Scholar
- 44.S.D. Odintsov, V.K. Oikonomou, A.V. Timoshkin, E.N. Saridakis, R. Myrzakulov, arXiv:1810.01276 [gr-qc]Google Scholar
- 45.S.D. Odintsov, V.K. Oikonomou, Phys. Rev. D 98, 024013 (2018) arXiv:1806.07295 [gr-qc]ADSCrossRefGoogle Scholar
- 46.S.D. Odintsov, V.K. Oikonomou, arXiv:1806.01588.01276 [gr-qc]Google Scholar
- 47.S.D. Odintsov, V.K. Oikonomou, arXiv:1711.02230v1 [gr-qc]Google Scholar
- 48.K. Bamba, Davood Momeni, Mudhahir Al Ajmi, arXiv:1711.10475v1Google Scholar
- 49.Mubasher Jamil, Kuralay Yesmakhanova, Davood Momeni, Ratbay Myrzakulov, Cent. Eur. J. Phys. 10, 1065 (2012)Google Scholar
- 50.K. Bamba, S. Nojiri, S.D. Odintsov, arXiv:1401.7378v2Google Scholar
- 51.Manuel Hohmann, Laur Järv, Ulbossyn Ualikhanova, arXiv:1706.02376v2 [gr-qc]Google Scholar
- 52.K. Hayashi, T. Shirafuji, Phys. Rev. D 19, 3524 (1979)ADSMathSciNetCrossRefGoogle Scholar
- 53.Di Liu, M.J. Rebouças, arXiv:1207.1503Google Scholar
- 54.Yi-Fu Cai, Shih-Hung Chen, James B. Dent, Sourish Dutta, Emmanuel N. Saridakis, arXiv:1104.4349v2 [astro-ph.CO]Google Scholar
- 55.Yi-Fu Cai, Chunlong Li, Emmanuel N. Saridakis, LingQin Xue, arXiv:1801.05827v1 [gr-qc]Google Scholar
- 56.B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 064035 (2011)ADSCrossRefGoogle Scholar
- 57.L.L. So, J.M. Nestr, arXiv:gr-qc/0612062Google Scholar
- 58.S.C. Ulhoa, E.P. Spaniol, arXiv:1303.144Google Scholar
- 59.Artur Alho, Sante Carloni, Claes Uggla, arXiv:1607.05715v2 [gr-qc]Google Scholar
- 60.Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, New York, 2003)Google Scholar
- 61.S.D. Odintsov, V.K. Oikonomou, Int. J. Mod. Phys. D 26, 1750085 (2017) arXiv:1512.04787 [gr-qc]ADSCrossRefGoogle Scholar
- 62.L. Nottale, Found. Sci. 15, 101.152 (2008)MathSciNetGoogle Scholar
- 63.M.H. Daouda, M.E. Rodrigues, M.J.S. Houndjo, Eur. Phys. J. C 72, 1893 (2012)ADSCrossRefGoogle Scholar
- 64.K. Karami, A. Abdolmaleki, arXiv:1202.2278Google Scholar
- 65.Mubasher Jamil, Davood Momeni, Ratbay Myrzakulov, arXiv:1309.3269v3 [gr-qc]Google Scholar
- 66.M. Jamil, D. Momeni, R. Myrzakulov, Eur. Phys. J. C 72, 1959 (2012)ADSCrossRefGoogle Scholar
- 67.S. Nesseris, S. Basilakos, E.N. Saridakis, L. Perivolaropoulos, arXiv:1308.6142v3 [astro-ph.CO]Google Scholar
- 68.W. El Hanafy, G.G.L. Nashed, arXiv:1410.2467v3 [hep-th]Google Scholar
- 69.S.D. Odintsov, V.K. Oikonomou, Phys. Rev. D 92, 124024 (2015) arXiv:1510.04333 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar