The distinctions between ΛCDM and f(T) gravity according to Noether symmetry

Regular Article - Theoretical Physics

Abstract

Noether’s theory offers us a useful tool to research the conserved quantities and symmetries of the modified gravity theories, among which the f(T) theory, a generally modified teleparallel gravity, has been proposed to account for the dark energy phenomena. By the Noether symmetry approach, we investigate the power-law, exponential and polynomial forms of f(T) theories. All forms of f(T) concerned in this work possess the time translational symmetry, which is related with energy condition or Hamilton constraint. In addition, we find that the performances of the power-law and exponential forms are not pleasing. It is rational adding a linear term T to T n as the most efficient amendment to resemble the teleparallel gravity or General Relativity on small scales, i.e., the scale of the solar system. The corresponding Noether symmetry indicates that only time translational symmetry remains. Through numerically calculations and observational data-sets constraining, the optimal form αT+βT −1 is obtained, whose cosmological solution resembles the standard ΛCDM best with lightly reduced cosmic age which can be alleviated by introducing another T m term. More important is that we find the significant differences between ΛCDM and f(T) gravity. The ΛCDM model has also two additional symmetries and corresponding positive conserved quantities, except the two negative conserved quantities.

Keywords

Dark Energy Hubble Constant Teleparallel Gravity Baryon Acoustic Oscillation Astrophysical Observation 

Notes

Acknowledgements

This work is partly supported by National Natural Science Foundation of China under Grant Nos. 11075078 and 10675062 and by the project of knowledge Innovation Program (PKIP) of Chinese Academy of Sciences (CAS) under the grant No. KJCX2.YW.W10 through the KITPC where we have initiated this present work. Han Dong would also like to thank his parents for the support to complete the Master’s graduate studies.

References

  1. 1.
    C.L. Bennett et al. (2012). arXiv:1212.5226
  2. 2.
    S. Perlmutter et al., Astrophys. J. 517, 565 (1999) ADSCrossRefGoogle Scholar
  3. 3.
    S.W. Allen et al., Mon. Not. R. Astron. Soc. 353, 457 (2004) ADSCrossRefGoogle Scholar
  4. 4.
    M. Tegmark et al., Phys. Rev. D 69, 103501 (2004) ADSCrossRefGoogle Scholar
  5. 5.
    D.J. Eisenstein et al., Astrophys. J. 633, 560 (2005) ADSCrossRefGoogle Scholar
  6. 6.
    M. Tegmark et al., Phys. Rev. D 69, 103501 (2004) ADSCrossRefGoogle Scholar
  7. 7.
    P.A.R. Ade et al. (Planck Collaboration) (2013). arXiv:1303.5076 [astro-ph.CO]
  8. 8.
    F. Perrotta, C. Baccigalupi, S. Matarrese, Phys. Rev. D 61, 023507 (1999) ADSCrossRefGoogle Scholar
  9. 9.
    S. Capozziello, V.F. Cardone, S. Carloni, A. Troisi, Int. J. Mod. Phys. D 12, 1969–1982 (2003) ADSCrossRefGoogle Scholar
  10. 10.
    T.P. Sotiriou, V. Faraoni (2008). arXiv:0805.1726
  11. 11.
    A.A. Starobinsky, JETP Lett. 86, 157 (2007) ADSCrossRefGoogle Scholar
  12. 12.
    S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    T. Multämaki, I. Vilja, Phys. Rev. D 74, 064022 (2006) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    T. Multämaki, I. Vilja, Phys. Rev. D 76, 064021 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    G.R. Bengochea, R. Ferraro, Phys. Rev. D 79, 124019 (2009) ADSCrossRefGoogle Scholar
  17. 17.
    E.V. Linder, Phys. Rev. D 81, 127301 (2010) ADSCrossRefGoogle Scholar
  18. 18.
    K. Bamba, S. Capozziello, S. Nojiri, S. Odintsov, Astrophys. Space Sci. 342, 155 (2012). arXiv:1205.3421 ADSCrossRefGoogle Scholar
  19. 19.
    K. Bamba, R. Myrzakulov, S. Nojiri, S. Odintsov, Phys. Rev. D 85, 104036 (2012). arXiv:1202.4057 ADSCrossRefGoogle Scholar
  20. 20.
    K. Bamba, C.-Q. Geng, J. Cosmol. Astropart. Phys. 1111, 008 (2011). arXiv:1109.1694 ADSCrossRefGoogle Scholar
  21. 21.
    R. Aldrovandi, J.G. Pereira, An Introduction to Teleparallel Gravity (Instituto de Fisica Teorica, UNSEP, Sao Paulo, 2007). http://www.ift.unesp.br/gcg/tele.pdf Google Scholar
  22. 22.
    J. Garechi (2010). arXiv:1010.2654
  23. 23.
    Z. Haghani, T. Harko, H.R. Sepangi, S. Shahidi, J. Cosmol. Astropart. Phys. 1210, 061 (2012). arXiv:1202.1879 ADSCrossRefGoogle Scholar
  24. 24.
    A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 217 (1928) Google Scholar
  25. 25.
    A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 224 (1928) Google Scholar
  26. 26.
    G.R. Bengochea, Phys. Lett. B 695, 405–411 (2011) ADSCrossRefGoogle Scholar
  27. 27.
    P. Wu, H. Yu, Phys. Lett. B 693, 415–420 (2010) MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    P. Wu, H. Yu, Phys. Lett. B 692, 176 (2010) MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 104017 (2011) ADSCrossRefGoogle Scholar
  30. 30.
    T.P. Sotiriou, B. Li, J.D. Barrow, Phys. Rev. D 83, 104030 (2011) ADSCrossRefGoogle Scholar
  31. 31.
    C.G. Böhmer, A. Mussa, N. Tamanini (2011). arXiv:1107.4455v2
  32. 32.
    Y.F. Cai, S.H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis (2011). arXiv:1104.4349
  33. 33.
    S.H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis, Phys. Rev. D 83, 023508 (2011) ADSCrossRefGoogle Scholar
  34. 34.
    J.B. Dent, S. Dutta, E.N. Saridakis, J. Cosmol. Astropart. Phys. 1101, 009 (2011) ADSCrossRefGoogle Scholar
  35. 35.
    Y.-F. Cai et al., Class. Quantum Gravity 28, 215011 (2011) ADSCrossRefGoogle Scholar
  36. 36.
    H. Dong, Y.-b. Wang, X.-h. Meng, Eur. Phys. J. C 72, 2201 (2012) ADSCrossRefGoogle Scholar
  37. 37.
    H. Dong, Y.-b. Wang, X.-h. Meng, Eur. Phys. J. C 72, 2002 (2012) ADSCrossRefGoogle Scholar
  38. 38.
    X.-h. Meng, Y.-b. Wang, Eur. Phys. J. C 71, 1755 (2011) ADSCrossRefGoogle Scholar
  39. 39.
    K. Bamba et al., J. Cosmol. Astropart. Phys. 1101, 021 (2011) ADSCrossRefGoogle Scholar
  40. 40.
    K. Bamba et al. (2010). arXiv:1008.4036
  41. 41.
    S. Capozziello, E. Piedipalumbo, C. Rubano, P. Scudellaro, Phys. Rev. D 80, 104030 (2009) ADSCrossRefGoogle Scholar
  42. 42.
    S. Capozziello, R. de Ritis, P. Scudellaro, Int. J. Mod. Phys. D 2, 463 (1993) ADSCrossRefMATHGoogle Scholar
  43. 43.
    S. Capozziello, S. Nesseris, L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 0712, 009 (2007) MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    B. Vakili, Phys. Lett. B 664, 16 (2008) MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    S. Capozziello, M. De Laurentis, S.D. Odintsov, Eur. Phys. J. C 72, 2068 (2012) ADSCrossRefGoogle Scholar
  46. 46.
    H. Wei, X.J. Guo, L.F. Wang, Phys. Lett. B 707, 298 (2012) ADSCrossRefGoogle Scholar
  47. 47.
    S. Capozziello, M. Demianski, R. de Ritis, C. Rubano, Phys. Rev. D 52, 3288 (1995) ADSCrossRefGoogle Scholar
  48. 48.
    S. Capozziello, R. De Ritis, P. Scudellaro, Int. J. Mod. Phys. D 3, 609 (1994) ADSCrossRefGoogle Scholar
  49. 49.
    B. Vakili, Phys. Lett. B 669, 206 (2008) MathSciNetADSCrossRefGoogle Scholar
  50. 50.
    P.J. Olver, Applications of Lie Groups to Differential Equations (1993) CrossRefMATHGoogle Scholar
  51. 51.
    L. Fatibene, M. Ferraris, M. Francavigilia, R.G. McLenagaghan, J. Math. Phys. 43, 3147 (2002) MathSciNetADSCrossRefMATHGoogle Scholar
  52. 52.
    L. Fatibene, M. Francaviglia, S. Mercadante (2001). arXiv:1001.2886
  53. 53.
    H.M. Sadjadi, Phys. Lett. B 718, 270 (2012). arXiv:1210.0937v2 ADSCrossRefGoogle Scholar
  54. 54.
    J. Simon, L. Verde, R. Jimenez, Phys. Rev. D 71, 123001 (2005) ADSCrossRefGoogle Scholar
  55. 55.
    D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, S.A. Standford, J. Cosmol. Astropart. Phys. 02, 008 (2010) ADSCrossRefGoogle Scholar
  56. 56.
    M. Moresco, A. Cimatti, R. Jimenez et al., J. Cosmol. Astropart. Phys. (2012). arXiv:1201.3609v1
  57. 57.
    E. Gaztanaga, A. Cabré, L. Hui, Mon. Not. R. Astron. Soc. 399, 1663 (2009) ADSCrossRefGoogle Scholar
  58. 58.
    C. Zhang, H. Zhang, S. Yuan, T.-J. Zhang, Y.-C. Sun (2012). arXiv:1207.4541 [astro-ph.CO]
  59. 59.
    C. Blake, S. Brough, M. Colless et al., Mon. Not. R. Astron. Soc. 425, 405 (2012). arXiv:1204.3674 [astro-ph.CO] ADSCrossRefGoogle Scholar
  60. 60.
    F. Beutler, C. Blake, M. Colless et al., Mon. Not. R. Astron. Soc. 416, 3017 (2011) ADSCrossRefGoogle Scholar
  61. 61.
    W.J. Percival, B.A. Reid, D.J. Eisenstein et al., Mon. Not. R. Astron. Soc. 401, 2148 (2010) ADSCrossRefGoogle Scholar
  62. 62.
    C. Blake, E.A. Kazin, F. Beutler et al., Mon. Not. R. Astron. Soc. 418, 1707 (2011) ADSCrossRefGoogle Scholar
  63. 63.
    N. Suzuki, D. Rubin, C. Lidman et al., Astrophys. J. 746, 85 (2012) ADSCrossRefGoogle Scholar
  64. 64.
    R.J. Yang, Europhys. Lett. 93, 60001 (2011) ADSCrossRefGoogle Scholar
  65. 65.
    L. Iorio, E.N. Saridakis, Mon. Not. R. Astron. Soc. 427, 1555 (2012) ADSCrossRefGoogle Scholar
  66. 66.
    M. Milgrom, Astrophys. J. 270, 365 (1983) ADSCrossRefGoogle Scholar
  67. 67.
    K. Sarkar, N. Sk, S. Ruz, S. Debnath, A.K. Sanyal, Int. J. Theor. Phys. (2013). arXiv:1201.2987v2 [astro-ph.CO]

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Department of physicsNankai UniversityTianjinChina
  2. 2.Kavli Institute of Theoretical Physics ChinaCASBeijingChina

Personalised recommendations