Skip to main content
Log in

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

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. C.L. Bennett et al. (2012). arXiv:1212.5226

  2. S. Perlmutter et al., Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  3. S.W. Allen et al., Mon. Not. R. Astron. Soc. 353, 457 (2004)

    Article  ADS  Google Scholar 

  4. M. Tegmark et al., Phys. Rev. D 69, 103501 (2004)

    Article  ADS  Google Scholar 

  5. D.J. Eisenstein et al., Astrophys. J. 633, 560 (2005)

    Article  ADS  Google Scholar 

  6. M. Tegmark et al., Phys. Rev. D 69, 103501 (2004)

    Article  ADS  Google Scholar 

  7. P.A.R. Ade et al. (Planck Collaboration) (2013). arXiv:1303.5076 [astro-ph.CO]

  8. F. Perrotta, C. Baccigalupi, S. Matarrese, Phys. Rev. D 61, 023507 (1999)

    Article  ADS  Google Scholar 

  9. S. Capozziello, V.F. Cardone, S. Carloni, A. Troisi, Int. J. Mod. Phys. D 12, 1969–1982 (2003)

    Article  ADS  Google Scholar 

  10. T.P. Sotiriou, V. Faraoni (2008). arXiv:0805.1726

  11. A.A. Starobinsky, JETP Lett. 86, 157 (2007)

    Article  ADS  Google Scholar 

  12. S. Nojiri, S.D. Odintsov, Phys. Rep. 505, 59 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  13. T. Multämaki, I. Vilja, Phys. Rev. D 74, 064022 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  14. T. Multämaki, I. Vilja, Phys. Rev. D 76, 064021 (2007)

    Article  ADS  Google Scholar 

  15. R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  16. G.R. Bengochea, R. Ferraro, Phys. Rev. D 79, 124019 (2009)

    Article  ADS  Google Scholar 

  17. E.V. Linder, Phys. Rev. D 81, 127301 (2010)

    Article  ADS  Google Scholar 

  18. K. Bamba, S. Capozziello, S. Nojiri, S. Odintsov, Astrophys. Space Sci. 342, 155 (2012). arXiv:1205.3421

    Article  ADS  Google Scholar 

  19. K. Bamba, R. Myrzakulov, S. Nojiri, S. Odintsov, Phys. Rev. D 85, 104036 (2012). arXiv:1202.4057

    Article  ADS  Google Scholar 

  20. K. Bamba, C.-Q. Geng, J. Cosmol. Astropart. Phys. 1111, 008 (2011). arXiv:1109.1694

    Article  ADS  Google Scholar 

  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. J. Garechi (2010). arXiv:1010.2654

  23. Z. Haghani, T. Harko, H.R. Sepangi, S. Shahidi, J. Cosmol. Astropart. Phys. 1210, 061 (2012). arXiv:1202.1879

    Article  ADS  Google Scholar 

  24. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 217 (1928)

  25. A. Einstein, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 224 (1928)

  26. G.R. Bengochea, Phys. Lett. B 695, 405–411 (2011)

    Article  ADS  Google Scholar 

  27. P. Wu, H. Yu, Phys. Lett. B 693, 415–420 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  28. P. Wu, H. Yu, Phys. Lett. B 692, 176 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  29. B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 104017 (2011)

    Article  ADS  Google Scholar 

  30. T.P. Sotiriou, B. Li, J.D. Barrow, Phys. Rev. D 83, 104030 (2011)

    Article  ADS  Google Scholar 

  31. C.G. Böhmer, A. Mussa, N. Tamanini (2011). arXiv:1107.4455v2

  32. Y.F. Cai, S.H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis (2011). arXiv:1104.4349

  33. S.H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis, Phys. Rev. D 83, 023508 (2011)

    Article  ADS  Google Scholar 

  34. J.B. Dent, S. Dutta, E.N. Saridakis, J. Cosmol. Astropart. Phys. 1101, 009 (2011)

    Article  ADS  Google Scholar 

  35. Y.-F. Cai et al., Class. Quantum Gravity 28, 215011 (2011)

    Article  ADS  Google Scholar 

  36. H. Dong, Y.-b. Wang, X.-h. Meng, Eur. Phys. J. C 72, 2201 (2012)

    Article  ADS  Google Scholar 

  37. H. Dong, Y.-b. Wang, X.-h. Meng, Eur. Phys. J. C 72, 2002 (2012)

    Article  ADS  Google Scholar 

  38. X.-h. Meng, Y.-b. Wang, Eur. Phys. J. C 71, 1755 (2011)

    Article  ADS  Google Scholar 

  39. K. Bamba et al., J. Cosmol. Astropart. Phys. 1101, 021 (2011)

    Article  ADS  Google Scholar 

  40. K. Bamba et al. (2010). arXiv:1008.4036

  41. S. Capozziello, E. Piedipalumbo, C. Rubano, P. Scudellaro, Phys. Rev. D 80, 104030 (2009)

    Article  ADS  Google Scholar 

  42. S. Capozziello, R. de Ritis, P. Scudellaro, Int. J. Mod. Phys. D 2, 463 (1993)

    Article  ADS  MATH  Google Scholar 

  43. S. Capozziello, S. Nesseris, L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 0712, 009 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  44. B. Vakili, Phys. Lett. B 664, 16 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  45. S. Capozziello, M. De Laurentis, S.D. Odintsov, Eur. Phys. J. C 72, 2068 (2012)

    Article  ADS  Google Scholar 

  46. H. Wei, X.J. Guo, L.F. Wang, Phys. Lett. B 707, 298 (2012)

    Article  ADS  Google Scholar 

  47. S. Capozziello, M. Demianski, R. de Ritis, C. Rubano, Phys. Rev. D 52, 3288 (1995)

    Article  ADS  Google Scholar 

  48. S. Capozziello, R. De Ritis, P. Scudellaro, Int. J. Mod. Phys. D 3, 609 (1994)

    Article  ADS  Google Scholar 

  49. B. Vakili, Phys. Lett. B 669, 206 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  50. P.J. Olver, Applications of Lie Groups to Differential Equations (1993)

    Book  MATH  Google Scholar 

  51. L. Fatibene, M. Ferraris, M. Francavigilia, R.G. McLenagaghan, J. Math. Phys. 43, 3147 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. L. Fatibene, M. Francaviglia, S. Mercadante (2001). arXiv:1001.2886

  53. H.M. Sadjadi, Phys. Lett. B 718, 270 (2012). arXiv:1210.0937v2

    Article  ADS  Google Scholar 

  54. J. Simon, L. Verde, R. Jimenez, Phys. Rev. D 71, 123001 (2005)

    Article  ADS  Google Scholar 

  55. D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, S.A. Standford, J. Cosmol. Astropart. Phys. 02, 008 (2010)

    Article  ADS  Google Scholar 

  56. M. Moresco, A. Cimatti, R. Jimenez et al., J. Cosmol. Astropart. Phys. (2012). arXiv:1201.3609v1

  57. E. Gaztanaga, A. Cabré, L. Hui, Mon. Not. R. Astron. Soc. 399, 1663 (2009)

    Article  ADS  Google Scholar 

  58. C. Zhang, H. Zhang, S. Yuan, T.-J. Zhang, Y.-C. Sun (2012). arXiv:1207.4541 [astro-ph.CO]

  59. C. Blake, S. Brough, M. Colless et al., Mon. Not. R. Astron. Soc. 425, 405 (2012). arXiv:1204.3674 [astro-ph.CO]

    Article  ADS  Google Scholar 

  60. F. Beutler, C. Blake, M. Colless et al., Mon. Not. R. Astron. Soc. 416, 3017 (2011)

    Article  ADS  Google Scholar 

  61. W.J. Percival, B.A. Reid, D.J. Eisenstein et al., Mon. Not. R. Astron. Soc. 401, 2148 (2010)

    Article  ADS  Google Scholar 

  62. C. Blake, E.A. Kazin, F. Beutler et al., Mon. Not. R. Astron. Soc. 418, 1707 (2011)

    Article  ADS  Google Scholar 

  63. N. Suzuki, D. Rubin, C. Lidman et al., Astrophys. J. 746, 85 (2012)

    Article  ADS  Google Scholar 

  64. R.J. Yang, Europhys. Lett. 93, 60001 (2011)

    Article  ADS  Google Scholar 

  65. L. Iorio, E.N. Saridakis, Mon. Not. R. Astron. Soc. 427, 1555 (2012)

    Article  ADS  Google Scholar 

  66. M. Milgrom, Astrophys. J. 270, 365 (1983)

    Article  ADS  Google Scholar 

  67. K. Sarkar, N. Sk, S. Ruz, S. Debnath, A.K. Sanyal, Int. J. Theor. Phys. (2013). arXiv:1201.2987v2 [astro-ph.CO]

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Han Dong.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dong, H., Wang, J. & Meng, X. The distinctions between ΛCDM and f(T) gravity according to Noether symmetry. Eur. Phys. J. C 73, 2543 (2013). https://doi.org/10.1140/epjc/s10052-013-2543-2

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjc/s10052-013-2543-2

Keywords

Navigation