Advertisement

Journal of High Energy Physics

, 2012:142 | Cite as

Matter density perturbations in modified teleparallel theories

  • Yi-Peng Wu
  • Chao-Qiang Geng
Article

Abstract

We study the matter density perturbations in modified teleparallel gravity theories, where extra degrees of freedom arise from the local Lorentz violation in the tangent space. We formulate a vierbein perturbation with variables addressing all the 16 components of the vierbein field. By assuming the perfect fluid matter source, we examine the cosmological implication of the 6 unfamiliar new degrees of freedom in modified f (T) gravity theories. We find that despite the new modes in the vierbein scenario provide no explicit significant effect in the small-scale regime, they exhibit some deviation from the standard general relativity results in super-horizon scales.

Keywords

Cosmology of Theories beyond the SM Classical Theories of Gravity 

References

  1. [1]
    A. Einstein, Riemannian Geometry with Maintaining the Notion of Distant Parallelism, Sitz. Preuss. Akad. Wiss. (1928) 217.Google Scholar
  2. [2]
    A. Einstein, New Possibility for a Unified Field Theory of Gravitation and Electricity, Sitz. Preuss. Akad. Wiss. (1928) 224.Google Scholar
  3. [3]
    A. Unzicker and T. Case, Translation of Einsteins attempt of a unified field theory with teleparallelism, physics/0503046 [INSPIRE].
  4. [4]
    K. Hayashi and T. Shirafuji, New General Relativity, Phys. Rev. D 19 (1979) 3524 [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    K. Hayashi and T. Shirafuji, Addendum toNew general relativity”, Phys. Rev. D 24 (1981) 3312.MathSciNetADSGoogle Scholar
  6. [6]
    J. Maluf, Hamiltonian formulation of the teleparallel description of general relativity, J. Math. Phys. 35 (1994) 335 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    R. Ferraro and F. Fiorini, Modified teleparallel gravity: Inflation without inflaton, Phys. Rev. D 75 (2007) 084031 [gr-qc/0610067] [INSPIRE].MathSciNetADSGoogle Scholar
  8. [8]
    R. Ferraro and F. Fiorini, On Born-Infeld Gravity in Weitzenbock spacetime, Phys. Rev. D 78 (2008) 124019 [arXiv:0812.1981] [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    R. Myrzakulov, Accelerating universe from F(T) gravity, Eur. Phys. J. C 71 (2011) 1752 [arXiv:1006.1120] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    G.R. Bengochea, Observational information for f(T) theories and Dark Torsion, Phys. Lett. B 695 (2011) 405 [arXiv:1008.3188] [INSPIRE].ADSGoogle Scholar
  11. [11]
    P. Wu and H.W. Yu, f (T) models with phantom divide line crossing, Eur. Phys. J. C 71 (2011) 1552 [arXiv:1008.3669] [INSPIRE].ADSGoogle Scholar
  12. [12]
    K. Bamba, C.-Q. Geng and C.-C. Lee, Comment onEinsteins Other Gravity and the Acceleration of the Universe”, arXiv:1008.4036 [INSPIRE].
  13. [13]
    K. Bamba, C.-Q. Geng, C.-C. Lee and L.-W. Luo, Equation of state for dark energy in f (T) gravity, JCAP 01 (2011) 021 [arXiv:1011.0508] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    K. Yerzhanov, S. Myrzakul, I. Kulnazarov and R. Myrzakulov, Accelerating cosmology in F (T) gravity with scalar field, arXiv:1006.3879 [INSPIRE].
  15. [15]
    P. Wu and H.W. Yu, Observational constraints on f (T) theory, Phys. Lett. B 693 (2010) 415 [arXiv:1006.0674] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    P. Wu and H.W. Yu, The dynamical behavior of f (T) theory, Phys. Lett. B 692 (2010) 176 [arXiv:1007.2348] [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    X.-c. Ao, X.-z. Li and P. Xi, Analytical approach of late-time evolution in a torsion cosmology, Phys. Lett. B 694 (2010) 186 [arXiv:1010.4117] [INSPIRE].MathSciNetADSGoogle Scholar
  18. [18]
    T. Wang, Static Solutions with Spherical Symmetry in f (T) Theories, Phys. Rev. D 84 (2011) 024042 [arXiv:1102.4410] [INSPIRE].ADSGoogle Scholar
  19. [19]
    Y. Zhang, H. Li, Y. Gong and Z.-H. Zhu, Notes on f (T) Theories, JCAP 07 (2011) 015 [arXiv:1103.0719] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    Y.-F. Cai, S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis, Matter Bounce Cosmology with the f (T) Gravity, Class. Quant. Grav. 28 (2011) 215011 [arXiv:1104.4349] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    R. Ferraro and F. Fiorini, Non trivial frames for f (T) theories of gravity and beyond, Phys. Lett. B 702 (2011) 75 [arXiv:1103.0824] [INSPIRE].MathSciNetADSGoogle Scholar
  22. [22]
    S. Chattopadhyay and U. Debnath, Emergent universe in chameleon, f (R) and f (T) gravity theories, Int. J. Mod. Phys. D 20 (2011) 1135 [arXiv:1105.1091] [INSPIRE].ADSGoogle Scholar
  23. [23]
    M. Sharif and S. Rani, F (T) Models within Bianchi Type I Universe, Mod. Phys. Lett. A 26 (2011) 1657 [arXiv:1105.6228] [INSPIRE].MathSciNetADSGoogle Scholar
  24. [24]
    H. Wei, X.-P. Ma and H.-Y. Qi, f (T) Theories and Varying Fine Structure Constant, Phys. Lett. B 703 (2011) 74 [arXiv:1106.0102] [INSPIRE].ADSGoogle Scholar
  25. [25]
    R. Ferraro and F. Fiorini, Cosmological frames for theories with absolute parallelism, Int. J. Mod. Phys. Conf. Ser. 3 (2011) 227 [arXiv:1106.6349] [INSPIRE].CrossRefGoogle Scholar
  26. [26]
    R.-X. Miao, M. Li and Y.-G. Miao, Violation of the first law of black hole thermodynamics in f (T) gravity, JCAP 11 (2011) 033 [arXiv:1107.0515] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    C.G. Boehmer, A. Mussa and N. Tamanini, Existence of relativistic stars in f (T) gravity, Class. Quant. Grav. 28 (2011) 245020 [arXiv:1107.4455] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    H. Wei, H.-Y. Qi and X.-P. Ma, Constraining f (T) Theories with the Varying Gravitational Constant, Eur. Phys. J. C 72 (2012) 2117 [arXiv:1108.0859] [INSPIRE].ADSGoogle Scholar
  29. [29]
    S. Capozziello, V. Cardone, H. Farajollahi and A. Ravanpak, Cosmography in f(T)-gravity, Phys. Rev. D 84 (2011) 043527 [arXiv:1108.2789] [INSPIRE].ADSGoogle Scholar
  30. [30]
    P. Wu and H. Yu, The Stability of the Einstein static state in f (T) gravity, Phys. Lett. B 703 (2011) 223 [arXiv:1108.5908] [INSPIRE].MathSciNetADSGoogle Scholar
  31. [31]
    M. Hamani Daouda, M.E. Rodrigues and M. Houndjo, Static Anisotropic Solutions in f (T) Theory, Eur. Phys. J. C 72 (2012) 1890 [arXiv:1109.0528] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    K. Bamba and C.-Q. Geng, Thermodynamics of cosmological horizons in f (T) gravity, JCAP 11 (2011) 008 [arXiv:1109.1694] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    R. Ferraro and F. Fiorini, Spherically symmetric static spacetimes in vacuum f(T) gravity, Phys. Rev. D 84 (2011) 083518 [arXiv:1109.4209] [INSPIRE].ADSGoogle Scholar
  34. [34]
    Y.-P. Wu and C.-Q. Geng, Primordial Fluctuations within Teleparallelism, arXiv:1110.3099 [INSPIRE].
  35. [35]
    P. Gonzalez, E.N. Saridakis and Y. Vasquez, Circularly symmetric solutions in three-dimensional Teleparallel, f (T) and Maxwell-f (T) gravity, JHEP 07 (2012) 053 [arXiv:1110.4024] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    K. Karami and A. Abdolmaleki, Holographic and new agegraphic f (T)-gravity models with power-law entropy correction, arXiv:1111.7269 [INSPIRE].
  37. [37]
    H. Wei, X.-J. Guo and L.-F. Wang, Noether Symmetry in f (T) Theory, Phys. Lett. B 707 (2012) 298 [arXiv:1112.2270] [INSPIRE].ADSGoogle Scholar
  38. [38]
    K. Atazadeh and F. Darabi, f (T) cosmology via Noether symmetry, Eur. Phys. J. C 72 (2012) 2016 [arXiv:1112.2824] [INSPIRE].ADSGoogle Scholar
  39. [39]
    H. Farajollahi, A. Ravanpak and P. Wu, Cosmic acceleration and phantom crossing in f (T)-gravity, Astrophys. Space Sci. 338 (2012) 23 [arXiv:1112.4700] [INSPIRE].CrossRefGoogle Scholar
  40. [40]
    K. Karami and A. Abdolmaleki, Generalized second law of thermodynamics in f(T)-gravity, JCAP 04 (2012) 007 [arXiv:1201.2511] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    K. Karami and A. Abdolmaleki, QCD ghost f (T)-gravity model, arXiv:1202.2278 [INSPIRE].
  42. [42]
    K. Bamba, R. Myrzakulov, S. Nojiri and S.D. Odintsov, Reconstruction of f (T) gravity: Rip cosmology, finite-time future singularities and thermodynamics, Phys. Rev. D 85 (2012) 104036 [arXiv:1202.4057] [INSPIRE].ADSGoogle Scholar
  43. [43]
    K. Bamba, M. Jamil, D. Momeni and R. Myrzakulov, Generalized Second Law of Thermodynamics in f (T) Cosmology with Power-Law and Logarithmic Corrected Entropies, arXiv:1202.6114 [INSPIRE].
  44. [44]
    D. Liu, P. Wu and H. Yu, Gódel-type universes in f(T) gravity, Int. J. Mod. Phys. D 21 (2012) 1250074 [arXiv:1203.2016] [INSPIRE].ADSGoogle Scholar
  45. [45]
    L. Iorio and E.N. Saridakis, Solar system constraints on f (T) gravity, arXiv:1203.5781 [INSPIRE].
  46. [46]
    N. Tamanini and C.G. Boehmer, Good and bad tetrads in f (T) gravity, Phys. Rev. D 86 (2012) 044009 [arXiv:1204.4593] [INSPIRE].ADSGoogle Scholar
  47. [47]
    A. Behboodi, S. Akhshabi and K. Nozari, Matter stability in modified teleparallel gravity, Phys. Lett. B 718 (2012) 30 [arXiv:1205.4570] [INSPIRE].ADSGoogle Scholar
  48. [48]
    H. Dong, Y.-B. Wang and X.-H. Meng, Birkhoffs Theorem in f (T) Gravity upto the Perturbative Order, Eur. Phys. J. 72 (2012) 2201 [arXiv:1205.6385] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    D. Liu and M. Reboucas, Energy conditions bounds on f(T) gravity, Phys. Rev. D 86 (2012) 083515 [arXiv:1207.1503] [INSPIRE].ADSGoogle Scholar
  50. [50]
    C.-Q. Geng, C.-C. Lee, E.N. Saridakis and Y.-P. Wu, ’TeleparallelDark Energy, Phys. Lett. B 704 (2011) 384 [arXiv:1109.1092] [INSPIRE].ADSGoogle Scholar
  51. [51]
    C.-Q. Geng, C.-C. Lee and E.N. Saridakis, Observational Constraints on Teleparallel Dark Energy, JCAP 01 (2012) 002 [arXiv:1110.0913] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    H. Wei, Dynamics of Teleparallel Dark Energy, Phys. Lett. B 712 (2012) 430 [arXiv:1109.6107] [INSPIRE].ADSGoogle Scholar
  53. [53]
    C. Xu, E.N. Saridakis and G. Leon, Phase-Space analysis of Teleparallel Dark Energy, JCAP 07 (2012) 005 [arXiv:1202.3781] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    J.-A. Gu, C.-C. Lee and C.-Q. Geng, Tracker Teleparallel Dark Energy with Purely Non-minimal Coupling to Gravity, arXiv:1204.4048 [INSPIRE].
  55. [55]
    B. Li, T.P. Sotiriou and J.D. Barrow, f (T) gravity and local Lorentz invariance, Phys. Rev. D 83 (2011) 064035 [arXiv:1010.1041] [INSPIRE].ADSGoogle Scholar
  56. [56]
    M. Li, R.-X. Miao and Y.-G. Miao, Degrees of freedom of f (T) gravity, JHEP 07 (2011) 108 [arXiv:1105.5934] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  57. [57]
    R.J. Yang, Conformal transformation in f (T) theories, Europhys. Lett. 93 (2011) 60001.ADSCrossRefGoogle Scholar
  58. [58]
    T.P. Sotiriou, B. Li and J.D. Barrow, Generalizations of teleparallel gravity and local Lorentz symmetry, Phys. Rev. D 83 (2011) 104030 [arXiv:1012.4039] [INSPIRE].ADSGoogle Scholar
  59. [59]
    B. Li, T.P. Sotiriou and J.D. Barrow, Large-scale Structure in f (T) Gravity, Phys. Rev. D 83 (2011) 104017 [arXiv:1103.2786] [INSPIRE].ADSGoogle Scholar
  60. [60]
    R. Aldrovandi and J.G. Pereira, An Introduction to Teleparallel Gravity, Instituto de Fisica Teorica, UNSEP, Sao Paulo [http://www.ift.unesp.br/gcg/tele.pdf].
  61. [61]
    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, New York, U.S.A. (1972).Google Scholar
  62. [62]
    S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis, Cosmological perturbations in f (T) gravity, Phys. Rev. D 83 (2011) 023508 [arXiv:1008.1250] [INSPIRE].ADSGoogle Scholar
  63. [63]
    J.B. Dent, S. Dutta and E.N. Saridakis, f (T) gravity mimicking dynamical dark energy. Background and perturbation analysis, JCAP 01 (2011) 009 [arXiv:1010.2215] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    J.-c. Hwang and H.-r. Noh, Gauge ready formulation of the cosmological kinetic theory in generalized gravity theories, Phys. Rev. D 65 (2002) 023512 [astro-ph/0102005] [INSPIRE].ADSGoogle Scholar
  65. [65]
    S. Tsujikawa, Matter density perturbations and effective gravitational constant in modified gravity models of dark energy, Phys. Rev. D 76 (2007) 023514 [arXiv:0705.1032] [INSPIRE].MathSciNetADSGoogle Scholar
  66. [66]
    S. Tsujikawa, K. Uddin and R. Tavakol, Density perturbations in f (R) gravity theories in metric and Palatini formalisms, Phys. Rev. D 77 (2008) 043007 [arXiv:0712.0082] [INSPIRE].MathSciNetADSGoogle Scholar
  67. [67]
    A.D. Felice and S. Tsujikawa, f (R) Theories, Living Rev. Relativ. 13 (2010) 3 [http://www.livingreviews.org/lrr-2010-3].
  68. [68]
    R. Zheng and Q.-G. Huang, Growth factor in f (T) gravity, JCAP 03 (2011) 002 [arXiv:1010.3512] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    X. Fu, P. Wu and H. Yu, The growth of matter perturbations in f (T) gravity, Int. J. Mod. Phys. D 20 (2011) 1301 [arXiv:1204.2333] [INSPIRE].ADSGoogle Scholar
  70. [70]
    L. Amendola and S. Tsujikawa, Dark Energy - Theory and Observations, Cambridge University Press, Cambridge, U.K. (2010).MATHGoogle Scholar
  71. [71]
    E.V. Linder and R.N. Cahn, Parameterized Beyond-Einstein Growth, Astropart. Phys. 28 (2007) 481 [astro-ph/0701317] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    G.R. Bengochea and R. Ferraro, Dark torsion as the cosmic speed-up, Phys. Rev. D 79 (2009) 124019 [arXiv:0812.1205] [INSPIRE].ADSGoogle Scholar
  73. [73]
    E.V. Linder, Einsteins Other Gravity and the Acceleration of the Universe, Phys. Rev. D 81 (2010) 127301 [Erratum ibid. D 82 (2010) 109902] [arXiv:1005.3039] [INSPIRE].ADSGoogle Scholar
  74. [74]
    E.V. Linder, Cosmic growth history and expansion history, Phys. Rev. D 72 (2005) 043529 [astro-ph/0507263] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Department of PhysicsNational Tsing Hua UniversityHsinchu, 300Taiwan
  2. 2.Physics Division, National Center for Theoretical SciencesHsinchu, 300Taiwan
  3. 3.College of Mathematics & PhysicsChongqing University of Posts & TelecommunicationsChongqingChina

Personalised recommendations