Authors
Abstract
According to the perturbation order, the equations of motion of low-energy string effective action are the generalized Einstein equations. Thus, by making use of the conformal transformation of the metric tensor, it is possible to map the low-energy string effective action into f(T) gravity, relating the dilaton field to the torsion scalar. Considering a homogeneous and isotropic universe and writing the canonical Lagrangian for f(T) gravity, we show that the invariance under the duality transformation holds for the cosmic scale factor a(t) at the level of the Lagrangian. Finally, by use of the dualized Lagrangian and also the invariance of torsion scalar under the scale factor duality a(t)→1/a(t), the specific form of the f(T) function is obtained.
Keywords
2. T H Buscher, B 194 (1987) 51; Phys. Lett. B 201 (1988) 466.
3. A Giveon, M Porrati and E Rabinovici, Phys. Rep. 244 (1994) 77.
4. A Giveon and M Rocek, Nucl. Phys. B 380 (1992) 128.
5. E Alvarez, L Alvarez-Gaume, and Y Lozano, Phys. Lett. B 336 (1994) 183.
6. M Rocek and E Verlinde, Nucl. Phys. B 373 (1992) 630.
7. S M Carroll, V Duvvuri, M Trodden, and M S Turner, Phys. Rev. D 70 (2004) 043528.
8. S Nojiri and S D Odintsov, Phys. Rev. D 74 (2006) 086005. S Nojiri and S D Odintsov, J. Phys. Conf. Ser. 66 (2007) 012005 ,hep-th/0611071; K Bamba, C Q Geng, S Nojiri, and S D Odintsov, Phys. Rev. D 79 (2009) 083014; K Bamba and C Q Geng, Prog. Theor. Phys. 122 (2009) 1267.
9. P Wu and H W Yu, Phys. Lett. B 693 (2010) 415; G R Bengochea, Phys. Lett. B 695 (2011) 405; S Basilakos, Phys. Rev. D 93 (2016) 083007; K Atazadeh and F Darabi, Eur. Phys. J. C 72 (2012) 2016; S Basilakos, S Capozziello, M De Laurentis, A Paliathanasis and M Tsamparlis, Phys. Rev. D 88 (2013) 103526; A Paliathanasis, S Basilakos, E N Saridakis, S Capozziello, K Atazadeh, F Darabi and M Tsamparlis, Phys. Rev. D 89 (2014) 104042; F Darabi, M Mousavi, and K Atazadeh, Phys. Rev. D 91 (2015) 084023; K Atazadeh and, A Eghbali, Phys. Scr. 90 (2015) 045001; K Atazadeh, and M Mousavi, Eur. Phys. J. C 73 (2013) 2272; S Capozziello, P A Gonzalez, E N Saridakis and Y Vasquez, Journal of High Energy Physics 02 (2013) 039; G. Contopoulos, B Grammaticos and A Ramani, J. Phys. A 25 (1993) 5795; J Demaret and C Scheen, J. Phys. A 29 (1996) 59; S Cotsakis, J Demaret, Y De Rop, and L Querella, Phys. Rev. D 48 (1993) 4595.
10. A Einstein, Sitz. Preuss. Akad. Wiss. (1928) 217; ibid p. 224.
11. S Capozziello and R de Ritis, Int. J. Mod. Phys. D 2 (1993) 367; B J Broy, F G Pedro, and A Westphal, Journal of High Energy Physicsics 03 (2015) 029.
12. S Capozziello, S J G Gionti, and D Vernieri, “Journal of Cosmology and Astroparticle Physics”, 01 (2016) 015.
13. M Wright, Phys. Rev. D 93 (2016) 103002
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