This thesis investigates models of dark energy based on generalized theories in the framework of the teleparallel equivalent of general relativity. We study the cosmic background evolution in the quintessence-inspired teleparallel dark energy model. We explore the cosmological perturbation of $f(T)$ gravity, and we analyze the similar perturbation scenario of teleparallel quintessence model. We check the viability of teleparallel dark energy theories in the weak-field regime through the parametrized post-Newtonian approach, and finally, we show that the Cauchy problem in the generalized teleparallel theory can be resolved by a time-gauge fixing condition.

[1] A.G. Riess, et al., Supernova Search Team Collaboration, Astron. J. 116, 1009 (1998); S. Perlmutter, et al., Supernova Cosmology Project Collaboration, Astrophys. J. 517, 565 (1999).
[2] PLANCK collaboration, P. A. R. Ade et al., [arXiv:1303.5082].
[3] T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010); A. De Felice and S. Tsujikawa, arXiv:1002.4928 [gr-qc].
[4] W. Hu and I. Sawicki, Phys. Rev. D76, 064004 (2007); A. A. Starobinsky, JETP Lett. 86, 157 (2007); S. Tsujikawa, Phys. Rev. D77, 023507 (2008); E. V. Linder, Phys. Rev. D80, 123528 (2009).
[5] B. Ratra, P. J. E. Peebles, Phys. Rev. D37, 3406 (1988); C. Wetterich, Nucl. Phys. B302, 668 (1988); A. R. Liddle, R. J. Scherrer, Phys. Rev. D59, 023509 (1999); I. Zlatev, L. -M. Wang, P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); Z. -K. Guo, N. Ohta, Y. -Z. Zhang, Phys. Rev. D72, 023504 (2005); S. Dutta, E. N. Saridakis, R. J. Scherrer, Phys. Rev. D79, 103005 (2009).
[6] J.P. Uzan, Phys. Rev. D59, 123510 (1999); N. Bartolo, M. Pietroni, Phys. Rev. D61, 023518 (2000); V. Faraoni, Phys. Rev. D62, 023504 (2000); E. Elizalde, S. Nojiri, S. Odintsov, Phys. Rev. D70, 043539 (2004).
[7] R. R. Caldwell, M. Kamionkowski, N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003); S. ’i. Nojiri, S. D. Odintsov, Phys. Lett. B562, 147 (2003); V. K. Onemli, R. P. Woodard, Phys. Rev. D70, 107301 (2004); S. Dutta and R. J. Scherrer, Phys. Lett. B676, 12 (2009). C. Kaeonikhom, B. Gumjudpai, E. N. Saridakis, Phys. Lett. B695, 45 (2011).
[8] P. G. Bergmann, Int. J. Theor. Phys. 1, 25 (1968); K. Nordtvedt, Astrophys. J. 161, 1059 (1970).
[9] Y. Fujii, K. -i. Maeda, The Scalar-Tensor Theory of Gravitation, Cambridge Univer- sity Press, UK (2003).
[10] A. Einstein, Sitz. Preuss. Akad. Wiss., 1928, p. 217; A. Einstein, Sitz. Preuss. Akad. Wiss., 1928, p. 224; A. Unzicker, T. Case, [arXiv:physics/0503046].
[11] K. Hayashi, T. Shirafuji, Phys. Rev. D19, 3524 (1979); K. Hayashi, T. Shirafuji, Phys. Rev. D24, 3312 (1982), Addendum.
[12] M. Schweizer, N. Straumann and A. Wipf, Gen. Relativ. Gravit. 12, 951 (1980); J. Nitsch and F. W. Hehl, Phys. Lett. B90, 98 (1980); R. Kuhfuss and J. Nitsch, Gen. Relativ. Gravit. 18, 1207 (1986).
[13] J. W. Maluf, J. Math. Phys. 35, 335 (1994).
[14] R. Aldrovandi and J. G. Pereira, Teleparallel Gravity: An Introduction (Fundamental
Theories of Physics) (Springer; 2013 edition).
[15] R. Ferraro and F. Fiorini, Phys. Rev. D75, 084031 (2007); Phys. Rev. D78, 124019
(2008).
[16] G. R. Bengochea and R. Ferraro, Phys. Rev. D79, 124019 (2009); E. V. Linder, Phys. Rev. D81, 127301 (2010); R. Myrzakulov, arXiv:1006.1120 [gr-qc]; G. R. Ben- gochea, Phys. Lett. B695, 405 (2011); P. Wu, H. W. Yu, Eur. Phys. J. C71, 1552 (2011); K. Bamba, C. Q. Geng, C. C. Lee, arXiv:1008.4036 [astro-ph.CO]; K. Bamba, C. Q. Geng, C. C. Lee, L. W. Luo, JCAP 1101, 021 (2011); K. K. Yerzhanov, S. R. Myrzakul, I. I. Kulnazarov and R. Myrzakulov, arXiv:1006.3879 [gr-qc].
[17] C. Q. Geng, C. C. Lee, E. N. Saridakis and Y. P. Wu, Phys. Lett. B704, 384 (2011).
[18] C. Q. Geng, C. C. Lee and E. N. Saridakis, JCAP 1201, 002 (2012); C. Q. Geng and Y. P. Wu, JCAP 1304, 033 (2013); G. Otalora, JCAP 1307, 044 (2013); G. Otalora, Phys. Rev. D88, 063505 (2013).
[19] V. C. de Andrade and J. G. Pereira, Phys. Rev. D56, 4689 (1997).
[20] T. Sotiriou and E. Barausse, Phys. Rev. D75 (2007) 084007.
[21] B. Li, T. P. Sotiriou and J. D. Barrow, Phys. Rev. D83, 064035 (2011).
[22] S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, New York, 1972.
[23] A. A. Starobinsky, Phys. Lett. B91, 99 (1980).
[24] J. D. Barrow, Nucl. Phys. B296, 697 (1988); T. Chiba, Phys. Lett. B575, 1 (2003); E. E. Flanagan, Class. Quant. Grav. 21, 417 (2004); T. P. Sotiriou, Class. Quant. Grav. 23, 5117 (2006).
[25] T. Futamase and K. I. Maeda, Phys. Rev. D39, 399 (1989).
[26] R.-J. Yang, Europhys. Lett. 93 60001 (2011).
[27] J. W. Maluf and F. F. Faria, Phys. Rev. D85, 027502 (2012).
[28] K. Bamba, S. D. Odintsov and D. S-Gomez, Phys. Rev. D88, 084042 (2013).
[29] G. Otalora, arXiv:1402.2256 [gr-qc].
[30] K. Bamba, C.Q. Geng, C.C. Lee, JCAP 1011 001 (2010).
[31] J. A. Gu, C. C. Lee and C. Q. Geng, Phys. Lett. B 718, 722 (2013); C. Q. Geng, J. A. Gu and C. C. Lee, Phys. Rev. D88, 024030 (2013).
[32] B. Li, T. P. Sotiriou and J. D. Barrow, Phys. Rev. D83, 104017 (2011).
[33] M. Li, R. X. Miao, Y. G. Miao, JHEP 07, 108 (2011).
[34] C. Q. Geng and Y. P. Wu, JCAP 04, 033 (2013).
[35] J. T. Li, Y. P. Wu and C. Q. Geng, Phys. Rev. D89, 044040 (2014).
[36] D. Wands, K. A. Malik, D. H. Lyth and A. R. Liddle, Phys. Rev. D62, 043527 (2000).
[37] Y. P. Wu and C. Q. Geng, JHEP 11, 142 (2012).
[38] S.-H. Chen, J. B. Dent, S. Dutta and E. N. Saridakis, Phys. Rev. D83, 023508 (2011); J. B. Dent, S. Dutta, E. N. Saridakis, JCAP 1101, 009 (2011).
[39] L. Amendola and S. Tsujikawa, Dark Energy - Theory and Observations, Cambridge University Press, 2010.
[40] A. D. Felice and S. Tsujikawa, Living Rev. Relativity, 13 (2010), 3.
[41] R. Zheng, Q. G. Huang, JCAP 1103, 002 (2011); X. Fu, P. Wu and H. Yu, Int. J. Mod. Phys. D20, 1301 (2011).
[42] E. V. Linder and R. N. Cahn, Astropart. Phys. 28, 481 (2007).
[43] E. V. Linder, Phys. Rev. D72, 043529 (2005).
[44] B. Boisseau, G. Esposito-Far`ese, D. Polarski and A. A. Starobinsky, Phys. Rev. Lett. 85, 2236 (2000).
[45] C. G. Boehmer, A. Mussa, N. Tamanini, 2011, Class. Quantum Gravity, 28, 245020; M. H. Daouda, M. E. Rodrigues, M. J. S. Houndjo, Eur. Phys. J. C, 71, 1817 (2011); Eur. Phys. J. C, 72, 1890 (2012); Phys. Lett. B715, 241 (2012).
[46] L. Iorio and E. N. Saridakis, Mon. Not. R. Astron. Soc. 427, 1555 (2012).
[47] G. J. Olmo, Phys. Rev. Lett. 95, 261102 (2005); G. J. Olmo, Phys. Rev. D72, 083505 (2005); L. Perivolaropoulos, Phys. Rev. D81, 047501 (2010); M. Hohmann, L. J ̈arv, P. Kuusk and E. Randla, Phys. Rev. D88, 084054 (2013).
[48] R. V. Wagoner, Phys. Rev. D1, 3209 (1970).
[49] R. V. Wagoner and C. M. Will, Astrophys. J. 210, 764 (1976) [Erratum-ibid. 215, 984 (1977)].
[50] A.S. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge Uni- versity Press, Cambridge 1924).
[51] H.P. Robertson, in Space Age Astronomy, ed. A.J. Deutsch and W.B. Klemperer (Cambridge University Press, Cambridge 1924).
[52] L.I. Schi↵, in Relativity Theory and Astrophysics. I. Relativity and Cosmol- ogy ed. J. Ehlers (Providence, R.I.: American Mathematical Society).
[53] B. Bertotti, L. Iess and P. Tortora, Nature 425, 374 (2003).
[54] J. G. Williams, S. G. Turyshev and D. H. Boggs, Phys. Rev. Lett. 93, 261101 (2004).
[55] S. Chandrasekhar, Astrophysical Journal, vol. 142, p.1488 (1965).
[56] C.M Will, Theory and Experiment in Gravitational Physics, revisited ed. (Cambridge University Press, Cambridge 1993).
[57] L. L. Smalley, Phys. Rev. D21, 328 (1980).
[58] M. P. Hobson, G. P. Efstathiou and A. N. Lasenby General Relativity: An Introduc-
tion for Physicists (Cambridge University Press, 2006).
[59] C. M. Will, Astrophys. J. 163, 611 (1971).
[60] Y. C. Ong, K. Izumi, J. M. Nester and P. Chen, Phys. Rev. D88, 024019 (2013).
[61] W. H. Cheng, D. C. Chern and J. M. Nester, Phys. Rev. D38, 2656 (1988); J. M. Nester, Classical Quantum Gravity 5, 1003 (1988).
[62] J. Schwinger, Phys. Rev. 130, 1253 (1963).
[63] Y. P. Wu and C. Q. Geng, Phys. Rev. D86, 104058 (2012).
[64] J. W. Maluf, J. Math. Phys. 36, 4242 (1995).
[65] M. Blagojevic, Gravitation and Gauge Symmetries, Institute of Physics Publishing, Bristol, 2001.
[66] J. W. Maluf and J. F. da Rocha-Neto, Phys. Rev. D64, 084014 (2001).
[67] R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
[68] V. F. Mukhanov, H. A. Feldman and R. H. Brandenberger, Phys. Rep. 215, 203 (1992).
[69] J. M. Maldacena, JHEP 0305, 013 (2003).
[70] R. Ferraro and F. Fiorini, Phys. Lett. B702, 75 (2011); Int. J. Mod. Phys. Conf. Ser. 3, 227 (2011).
[71] C. Germani and A. Kehagias, Phys. Rev. Lett. 105, 011302 (2010); JCAP 05, 019 (2010).
[72] T. Kobayashi, M. Yamaguchi and J. Yokoyama, Prog. Theor. Phys. 126, 511 (2011).
[73] K. Izumi and Y. C. Ong, JCAP 06, 029 (2013).