Document Type : Original Article
Author
Department of Physics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran
Abstract
In this paper, we study the validity of the laws of thermodynamics in the form of a far parallel gravitational theory with an incomplete coupling between curves and scalar fields. To this end, we consider the FRW flat world, showing that the first and second laws of thermodynamics lie in its dynamic apparent horizon. We further assume that the universe is enclosed by the cosmological event horizon, such that in this case the first law of thermodynamics is valid, but the second law of thermodynamics is applied to the selected incomplete model, depending on the energy-momentum tensor components derived.
Keywords
- D N Spergel, et al., Astrophys. J. Suppl. 170 (2007) 377.
- S Perlmutter, et al., Astrophys. J. 598 (2003) 102.
- E Hawkins, et al., Mon. Not. Roy. Astron. Soc. 346 (2003) 78.
- D J Eisentein, et al., Astrophys. J. 633 (2005) 560.
- B Jain and A Taylor, Phys. Rev. Lett. 91 (2003) 141302.
- E J Copeland, M Sami and S Tsujikawa, Int. J. Mod. Phys. D 15 (2006) 1753.
- T P Sotiriou and V Faraoni, Rev. Mod. Phys. 82 (2010) 451.
- A Einsteinz, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 217 (1928) 224.
- K Hayashi and T Shirafuji, Phys. Rev. D. 19 (1979) 3524.
10. E V Linder, Phys. Rev. D. 81 (2010) 127301.
11. R Ferraro and F Fiorini, Phys. Rev. D. 75 (2007) 084031.
12. G R Bengochea and R Ferraro, Phys. Rev. D. 79 (2009) 124019 .
13. P Wu and H Yu, Phys. Lett. B 692 (2010) 176.
14. P Wu and H Yu, Eur .Phys. J. C 71 (2011) 1552.
15. م عطازاده و ع اقبالی، مجلة پژوهش فیزیک ایران 18 1 (۱۳۹۷) ۲۳.
15. M Atazadeh and A Eghbali, Iranian J. Phys. Res. 18 1 (2018) 23.
16. M R Setare and N Mohammadipour, JCAP 1211 (2012) 030.
17. Sh Chen, J B Dent, Sourish Dutta and E N Saridakis, Phys. Rev. D. 83 (2011) 023508.
18. C -Q Geng, C -C Lee, E N Saridakis and Y -P Wu, Phys. Lett. B 704 (2011) 384.
19. G Otalora, JCAP 1307 (2013) 044.
20. G Otalora, Phys. Rev. D. 88 (2013) 063505.
21. C -Q Geng, J -A Gu and C -C Lee, Phys. Rev. D. 88 (2013) 024030.
22. H M Sadjadi, Phys. Rev. D. 87 (2013) 064028.
23. S W Hawking, Com. Math. Phys. 43 (1975) 199.
24. J D Bekenstein, Phys. Rev. D. 7 (1973) 2333.
25. T Jacobson, Phys. Rev Lett. 75 (1995) 1260.
26. R G Cai and S P Kim, JHEP 02 (2005) 050.
27. M Akbar and R G Cai, Phys. Rev. D. 75 (2007) 084003.
28. C Eling, R Guedens and T Jacobson, Phys. Rev. Lett. 86 (2006) 121301.
29. A Sheykhi, B Wang and R-G Cai, Nucl. Phys. B. 779 (2007) 1.
30. M Akbar and R G Cai, Phys. Lett. B. 648 (2007) 243.
31. Y Gong and A Wang, Phys. Rev. Lett. 99 (2007) 211301.
32. A Sheykhi, JCAP 05 (2009) 019.
33. K Bamba and C Q Geng, Phys. Lett. B 679 (2009) 282.
34. K Karami and S Ghaffari, Phys. Lett. B 688 (2010) 125.
35. م آقائی آبچویه، ب میرزا و ح نادی، مجلة پژوهش فیزیک ایران 14 4 (۱۳۹3) ۲9۳.
35. M Aghaei Abchouyeh, B Mirza, B Mirza, and H Nadi, Iranian J. Phys. Res. 14 4 (2015) 293.
36. T Azizi and N Borhani, Astrophys. Space Sci. 357 (2015) 146.
37. T Azizi and N Borhani, Adv. High Energy Phys. 2017 (2017) 6839050.
38. B Wang, Y. Gong and E. Abdalla, Phys. Lett. B. 624 (2005) 141.
39. N Mazumder and S Chakraborty, Class. Quant. Grav. 26 (2009) 195016.
40. N Mazumder and S Chakraborty, Gen. Rel. Grav. 42 (2010) 813.
41. S A Hayward, Class. Quant. Grav. 15 (1998) 3147.
F Q Tu and Yi Xin. Chen, EPJC 76 (2016) 28
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