Abstract
In this paper, we investigate the Noether symmetries of F(T) cosmology involving matter and dark energy. In this model, the dark energy is represented by a canonical scalar field with a potential. Two special cases for dark energy are considered, including phantom energy and quintessence. We obtain F(T)∼T 3/4, and the scalar potential V(ϕ)∼ϕ 2 for both models of dark energy and discuss quantum picture of this model. Some astrophysical implications are also discussed.
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C.L. Bennett et al., Astrophys. J. Suppl. Ser. 148, 1 (2003)
D.N. Spergel et al., Astrophys. J. Suppl. Ser. 148, 175 (2003)
D.N. Spergel et al., Astrophys. J. Suppl. Ser. 170, 377 (2007)
S. Perlmutter et al., Astrophys. J. 483, 565 (1997)
S. Perlmutter et al., Nature 391, 51 (1998)
S. Perlmutter et al., Astrophys. J. 517, 565 (1999)
A.G. Riess et al., Astrophys. J. 607, 665 (2004)
A.G. Riess et al., Astrophys. J. 659, 98 (2007)
D.J. Eisentein et al., Astrophys. J. 633, 560 (2005)
B. Jain, A. Taylor, Phys. Rev. Lett. 91, 141302 (2003)
E. Hawkins et al., Mon. Not. R. Astron. Soc. 346, 78 (2003)
M. Tegmark et al., Phys. Rev. D 69, 103501 (2004)
S. Cole et al., Mon. Not. R. Astron. Soc. 362, 505 (2005)
L. Smolin, The Trouble with Physics (Houghton Mifflin Harcourt, Boston, 2006)
L. Amendola, S. Tsujikawa, Dark Energy: Theory and Observations (Cambridge University Press, Cambridge, 2010)
E.J. Copeland, M. Sami, S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006)
S. Capozziello, M. De Laurentis, arXiv:1108.6266v2 [gr-qc]
S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011)
T. Padmanabhan, Gen. Relativ. Gravit. 40, 529 (2008)
A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl., 217 (1928)
A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl., 224 (1928)
A. Einstein, Math. Ann. 102, 685 (1930)
K. Hayashi, T. Shirafuji, Phys. Rev. D 19, 3524 (1979) (See A. Unzicker and T. Case, arXiv:physics/0503046 for English translation.) Addendum-ibid. D 24 (1981) 3312
A. Unzicker, T. Case, arXiv:physics/0503046
R. Aldrovandi, J.G. Pereira, Instituto de Fisica Teorica, UNSEP, Sao Paulo. http://www.ift.unesp.br/gcg/tele.pdf
M. Li, R.X. Miao, Y.G. Miao, J. High Energy Phys. 1107, 108 (2011)
B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 064035 (2011)
T.P. Sotiriou, B. Li, J.D. Barrow, Phys. Rev. D 83, 104030 (2011)
P. Wu, H.W. Yu, Phys. Lett. B 693, 415 (2010)
R. Myrzakulov, Eur. Phys. J. C 71, 1752 (2011)
K.K. Yerzhanov, S.R. Myrzakul, I.I. Kulnazarov, R. Myrzakulov, arXiv:1006.3879
P. Wu, H. Yu, Phys. Lett. B 692, 176 (2010)
P.Y. Tsyba, I.I. Kulnazarov, K.K. Yerzhanov, R. Myrzakulov, Int. J. Theor. Phys. 50, 1876 (2011)
G.R. Bengochea, Phys. Lett. B 695, 405 (2011)
P. Wu, H.W. Yu, Eur. Phys. J. C 71, 1552 (2011)
R. Myrzakulov, arXiv:1008.4486
R.J. Yang, Europhys. Lett. 93, 60001 (2011)
K. Bamba, R. Myrzakulov, S. Nojiri, S.D. Odintsov, Phys. Rev. D 85, 104036 (2012). arXiv:1202.4057
M. Jamil, D. Momeni, R. Myrzakulov, Eur. Phys. J. C 72, 2075 (2012)
M. Jamil, K. Yesmakhanova, D. Momeni, R. Myrzakulov, Cent. Eur. J. Phys. doi:10.2478/s11534-012-0103-2
Y. Zhang, H. Li, Y. Gong, Z.H. Zhu, J. Cosmol. Astropart. Phys. 1107, 015 (2011)
M. Jamil, D. Momeni, R. Myrzakulov, Eur. Phys. J. C 72, 1959 (2012)
K. Bamba, M. Jamil, D. Momeni, R. Myrzakulov, arXiv:1202.6114
H. Wei, X.P. Ma, H.Y. Qi, Phys. Lett. B 703, 74 (2011)
C.G. Boehmer, A. Mussa, N. Tamanini, arXiv:1107.4455
K. Bamba, C.Q. Geng, C.C. Lee, L.W. Luo, J. Cosmol. Astropart. Phys. 1101, 021 (2011)
R. Zheng, Q.G. Huang, J. Cosmol. Astropart. Phys. 1103, 002 (2011)
R. Ferraro, F. Fiorini, Phys. Lett. B 702, 75 (2011)
R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)
R. Ferraro, F. Fiorini, Phys. Rev. D 78, 124019 (2008)
E. Noether, Nachr. D. König. Gesellsch. D. Wiss. Zu Goeöttingen Math.-Phys. Kl., 235 (1918). arXiv:physics/0503066
H. Wei, X.J. Guo, L.F. Wang, Phys. Lett. B 707, 298 (2012)
M. Jamil, F.M. Mahomed, D. Momeni, Phys. Lett. B 702, 315 (2011)
I. Hussain, M. Jamil, F.M. Mahomed, Astrophys. Space Sci. 337, 373 (2012)
M. Jamil, S. Ali, D. Momeni, R. Myrzakulov, Eur. Phys. J. C 72, 1998 (2012)
S. Capozziello, R. De Ritis, P. Scudellaro, Nuovo Cimento B 109, 159 (1994)
S. Capozziello, R. De Ritis, P. Scudellaro, Int. J. Mod. Phys. D 3, 609 (1994)
S. Capozziello, V.I. Manko, G. Marmo, C. Stornaiolo, Gen. Relativ. Gravit. 40, 2627 (2008)
B. Vakili, F. Khazaie, arXiv:1109.3352 [gr-qc]
B. Vakili, Phys. Lett. B 669, 206 (2008)
M. Jamil, D. Momeni, K. Bamba, R. Myrzakulov, Int. J. Mod. Phys. D 21, 1250065 (2012)
M. Jamil, D. Momeni, Chin. Phys. Lett. 28, 099801 (2011)
M.R. Setare, D. Momeni, Int. J. Theor. Phys. 51, 198 (2012)
M.R. Setare, D. Momeni, Int. J. Mod. Phys. D 19, 2079 (2010)
M. Jamil, D. Momeni, M. Raza, R. Myrzakulov, Eur. Phys. J. C 72, 1999 (2012)
M. Jamil, Y. Myrzakulov, O. Razina, R. Myrzakulov, Astrophys. Space Sci. 336, 315 (2011)
M. Jamil, I. Hussain, M.U. Farooq, Astrophys. Space Sci. 335, 339 (2011)
M. Jamil, I. Hussain, Int. J. Theor. Phys. 50, 465 (2011)
M.R. Setare, M. Jamil, Europhys. Lett. 92, 49003 (2010)
A. Sheykhi, M. Jamil, Phys. Lett. B 694, 284 (2011)
M. Jamil, M. Akbar, Gen. Relativ. Gravit. 43, 1061 (2011)
M. Jamil, Int. J. Theor. Phys. 49, 144 (2010)
M. Jamil, M.A. Rashid, Eur. Phys. J. C 60, 141 (2009)
F. De Paolis, M. Jamil, A. Qadir, Int. J. Theor. Phys. 49, 621 (2010)
Y. Zhang, Y.-G. Gong, Z.-H. Zhu, Phys. Lett. B 688, 13 (2010)
H. Wei, X.-J. Guo, L.-F. Wang, Phys. Lett. B 707, 298 (2012)
R. Kallosh, A. Linde, J. Cosmol. Astropart. Phys. 11, 011 (2010)
S. Capozziello, V.F. Cardone, H. Farajollahi, A. Ravanpak, Phys. Rev. D 84, 043527 (2011)
Acknowledgements
We would like to thank S.H. Hendi for useful communications and the anonymous reviewer for enlightening comments related to this work.
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Jamil, M., Momeni, D. & Myrzakulov, R. Noether symmetry of F(T) cosmology with quintessence and phantom scalar fields. Eur. Phys. J. C 72, 2137 (2012). https://doi.org/10.1140/epjc/s10052-012-2137-4
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DOI: https://doi.org/10.1140/epjc/s10052-012-2137-4