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Cosmological perturbations in f(T) gravity

Shih-Hung Chen1,*, James B. Dent1,†, Sourish Dutta2,‡, and Emmanuel N. Saridakis3,§

  • 1Department of Physics and School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287-1404, USA
  • 2Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
  • 3College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, People’s Republic of China

  • *schen102@asu.edu
  • †jbdent@asu.edu
  • ‡sourish.d@gmail.com
  • §msaridak@phys.uoa.gr
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Phys. Rev. D 83, 023508 – Published 10 January, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.023508

Abstract

We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbein, we extract the corresponding dispersion relation, which provides a constraint on the f(T) Ansätze that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100  Mpc) or larger), the evolution of matter overdensity will differ from ΛCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.

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References (33)

  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); C. L. Bennett et al., Astrophys. J. Suppl. Ser. 148, 1 (2003); M. Tegmark et al. (SDSS Collaboration), Phys. Rev. D 69, 103501 (2004); S. W. Allen et al., Mon. Not. R. Astron. Soc. 353, 457 (2004).
  2. P. J. Peebles and B. Ratra, Rev. Mod. Phys. 75, 559 (2003).
  3. B. Ratra and P. J. E. Peebles, Phys. Rev. D 37, 3406 (1988); C. Wetterich, Nucl. Phys. B302, 668 (1988); A. R. Liddle and R. J. Scherrer, Phys. Rev. D 59, 023509 (1998); I. Zlatev, L. M. Wang, and P. J. Steinhardt, Phys. Rev. Lett. 82, 896 (1999); Z. K. Guo, N. Ohta, and Y. Z. Zhang, Mod. Phys. Lett. A 22, 883 (2007); S. Dutta and R. J. Scherrer, Phys. Rev. D 78, 123525 (2008); 78, 083512 (2008); D. C. Dai, S. Dutta, and D. Stojkovic, 80, 063522 (2009); S. Dutta, S. D. H. Hsu, D. Reeb, and R. J. Scherrer, 79, 103504 (2009); S. Dutta, E. N. Saridakis, and R. J. Scherrer, 79, 103005 (2009); S. Dutta and R. J. Scherrer, Phys. Lett. B 676, 12 (2009).
  4. R. R. Caldwell, Phys. Lett. B 545, 23 (2002); R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003); S. Nojiri and S. D. Odintsov, Phys. Lett. B 562, 147 (2003); P. Singh, M. Sami, and N. Dadhich, Phys. Rev. D 68, 023522 (2003); J. M. Cline, S. Jeon, and G. D. Moore, 70, 043543 (2004); V. K. Onemli and R. P. Woodard, 70, 107301 (2004); W. Hu, 71, 047301 (2005); M. R. Setare and E. N. Saridakis, J. Cosmol. Astropart. Phys. 03 (2009) 002; E. N. Saridakis, Nucl. Phys. B819, 116 (2009); S. Dutta and R. J. Scherrer, Phys. Lett. B 676, 12 (2009).
  5. B. Feng, X. L. Wang, and X. M. Zhang, Phys. Lett. B 607, 35 (2005); Z. K. Guo et al., 608, 177 (2005); M.-Z Li, B. Feng, and X.-M Zhang, J. Cosmol. Astropart. Phys. 12 (2005) 002; B. Feng, M. Li, Y.-S. Piao, and X. Zhang, Phys. Lett. B 634, 101 (2006); W. Zhao and Y. Zhang, Phys. Rev. D 73, 123509 (2006); M. R. Setare and E. N. Saridakis, Phys. Lett. B 668, 177 (2008); Y. F. Cai, E. N. Saridakis, M. R. Setare, and J. Q. Xia, Phys. Rep. 493, 1 (2010).
  6. T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010); A. De Felice and S. Tsujikawa, Living Rev. Relativity 13, 3 (2010).
  7. S. Nojiri and S. D. Odintsov, Phys. Lett. B 631, 1 (2005); J. Phys. Conf. Ser. 66, 012005 (2007).
  8. P. Binétruy, C. Deffayet, and D. Langlois, Nucl. Phys. B565, 269 (2000); R. G. Cai, Y. G. Gong, and B. Wang, J. Cosmol. Astropart. Phys. 03 (2006) 006; Y. G. Gong and A. Wang, Classical Quantum Gravity 23, 3419 (2006); F. K. Diakonos and E. N. Saridakis, J. Cosmol. Astropart. Phys. 02 (2009) 030.
  9. S. Tsujikawa, arXiv:1004.1493.
  10. S. D. H. Hsu, Phys. Lett. B 594, 13 (2004); M. Li, 603, 1 (2004); Q. G. Huang and M. Li, J. Cosmol. Astropart. Phys. 08 (2004) 013; M. Ito, Europhys. Lett. 71, 712 (2005); X. Zhang and F. Q. Wu, Phys. Rev. D 72, 043524 (2005); D. Pavon and W. Zimdahl, Phys. Lett. B 628, 206 (2005); E. Elizalde, S. Nojiri, S. D. Odintsov, and P. Wang, Phys. Rev. D 71, 103504 (2005); E. N. Saridakis, Phys. Lett. B 660, 138 (2008).
  11. P. Horava, Phys. Rev. D 79, 084008 (2009); G. Calcagni, J. High Energy Phys. 09 (2009) 112; E. Kiritsis and G. Kofinas, Nucl. Phys. B821, 467 (2009); H. Lu, J. Mei, and C. N. Pope, Phys. Rev. Lett. 103, 091301 (2009); E. N. Saridakis, Eur. Phys. J. C 67, 229 (2010); X. Gao, Y. Wang, R. Brandenberger, and A. Riotto, Phys. Rev. D 81, 083508 (2010); G. Leon and E. N. Saridakis, J. Cosmol. Astropart. Phys. 11 (2009) 006; M. i. Park, J. High Energy Phys. 09 (2009) 123; S. Dutta and E. N. Saridakis, J. Cosmol. Astropart. Phys. 01 (2010) 013; C. Germani, A. Kehagias, and K. Sfetsos, J. High Energy Phys. 09 (2009) 060; E. Kiritsis, Phys. Rev. D 81, 044009 (2010); D. Capasso and A. P. Polychronakos, J. High Energy Phys. 02 (2010) 068; S. Dutta and E. N. Saridakis, J. Cosmol. Astropart. Phys. 05 (2010) 013; G. Koutsoumbas and P. Pasipoularides, Phys. Rev. D 82, 044046 (2010); M. Eune and W. Kim, 82, 124048 (2010).
  12. R. Ferraro and F. Fiorini, Phys. Rev. D 75, 084031 (2007).
  13. G. R. Bengochea and R. Ferraro, Phys. Rev. D 79, 124019 (2009).
  14. E. V. Linder, Phys. Rev. D 81, 127301 (2010).
  15. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 217 (1928); Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl.224; A. Unzicker and T. Case, arXiv:physics/0503046.
  16. K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979); 24, 3312 (1981).
  17. R. Myrzakulov, arXiv:1006.1120.
  18. J. B. Dent, S. Dutta, and E. N. Saridakis, arXiv:1010.2215.
  19. K. K. Yerzhanov, S. R. Myrzakul, I. I. Kulnazarov, and R. Myrzakulov, arXiv:1006.3879.
  20. P. Wu and H. Yu, Phys. Lett. B 692, 176 (2010).
  21. P. Wu and H. Yu, Phys. Lett. B 693, 415 (2010).
  22. R. Weitzenböck, Invarianten Theorie (Nordhoff, Groningen, 1923).
  23. J. W. Maluf, J. Math. Phys. 35, 335 (1994).
  24. H. I. Arcos and J. G. Pereira, Int. J. Mod. Phys. D 13, 2193 (2004).
  25. S. Weinberg, Cosmology (Oxford University Press Inc., New York, 2008).
  26. B. Li, T. P. Sotiriou, and J. D. Barrow, arXiv:1010.1041.
  27. T. Koivisto and D. F. Mota, Phys. Rev. D 73, 083502 (2006); G. Leon and E. N. Saridakis, arXiv:1007.3956; E. Calabrese, R. de Putter, D. Huterer, E. V. Linder, and A. Melchiorri, arXiv:1010.5612.
  28. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973).
  29. J. B. Dent and S. Dutta, Phys. Rev. D 79, 063516 (2009).
  30. C. Charmousis, G. Niz, A. Padilla, and P. M. Saffin, J. High Energy Phys. 08 (2009) 070; M. Li and Y. Pang, 08 (2009) 015; C. Bogdanos and E. N. Saridakis, Classical Quantum Gravity 27, 075005 (2010); D. Blas, O. Pujolas, and S. Sibiryakov, Phys. Rev. Lett. 104, 181302 (2010); K. Koyama and F. Arroja, J. High Energy Phys. 03 (2010) 061.
  31. G. J. Olmo, Phys. Rev. D 75, 023511 (2007).
  32. T. Koivisto and H. Kurki-Suonio, Classical Quantum Gravity 23, 2355 (2006); T. Koivisto, Phys. Rev. D 73, 083517 (2006); B. Li, J. D. Barrow, and D. F. Mota, 76, 104047 (2007); A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto, 77, 123515 (2008); AIP Conf. Proc. 1122, 252 (2009); T. S. Koivisto, Phys. Rev. D 82, 044022 (2010); A. de la Cruz Dombriz, arXiv:1004.5052.
  33. X. Gao, Y. Wang, R. Brandenberger, and A. Riotto, Phys. Rev. D 81, 083508 (2010).

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Phys. Rev. D 83, 023508– Published 10 January, 2011
  • Received 30 August 2010

© 2011 The American Physical Society

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