The European Physical Journal C

, Volume 70, Issue 1–2, pp 373–379 | Cite as

f(R,L m ) gravity

Regular Article - Theoretical Physics

Abstract

We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.

Keywords

Dark Matter Dark Energy Quantum Gravity Gravity Model Test Particle 

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References

  1. 1.
    A.G. Riess et al., Astron. J. 116, 1009 (1998) ADSCrossRefGoogle Scholar
  2. 2.
    S. Perlmutter et al., Astrophys. J. 517, 565 (1999) ADSCrossRefGoogle Scholar
  3. 3.
    P. de Bernardis et al., Nature 404, 955 (2000) ADSCrossRefGoogle Scholar
  4. 4.
    S. Hanany et al., Astrophys. J. 545, L5 (2000) ADSCrossRefGoogle Scholar
  5. 5.
    P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    T. Padmanabhan, Phys. Rep. 380, 235 (2003) MATHMathSciNetADSCrossRefGoogle Scholar
  7. 7.
    H.A. Buchdahl, Mon. Not. R. Astron. Soc. 150, 1 (1970) ADSGoogle Scholar
  8. 8.
    R. Kerner, Gen. Relativ. Gravit. 14, 453 (1982) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    J.P. Duruisseau, R. Kerner, P. Eysseric, Gen. Relativ. Gravit. 15, 797 (1983) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    J.D. Barrow, A.C. Ottewill, J. Phys. A: Math. Gen. 16, 2757 (1983) MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    H. Kleinert, H.-J. Schmidt, Gen. Relativ. Gravit. 34, 1295 (2002) MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    S.M. Carroll, V. Duvvuri, M. Trodden, M.S. Turner, Phys. Rev. D 70, 043528 (2004) ADSCrossRefGoogle Scholar
  13. 13.
    S. Capozziello, S. Nojiri, S.D. Odintsov, A. Troisi, Phys. Lett. B 639, 135 (2006) ADSCrossRefGoogle Scholar
  14. 14.
    L. Amendola, D. Polarski, S. Tsujikawa, Phys. Rev. Lett. 98, 131302 (2007) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    S. Capozziello, S. Nojiri, S.D. Odintsov, A. Troisi, Phys. Lett. B 639, 135 (2006) ADSCrossRefGoogle Scholar
  16. 16.
    S. Nojiri, S.D. Odintsov, Phys. Rev. D 74, 086005 (2006) MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    M. Amarzguioui, O. Elgaroy, D.F. Mota, T. Multamaki, Astron. Astrophys. 454, 707 (2006) MATHADSCrossRefGoogle Scholar
  18. 18.
    L. Amendola, R. Gannouji, D. Polarski, S. Tsujikawa, Phys. Rev. D 75, 083504 (2007) ADSCrossRefGoogle Scholar
  19. 19.
    T. Koivisto, Phys. Rev. D 76, 043527 (2007) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    A.A. Starobinsky, JETP Lett. 86, 157 (2007) ADSCrossRefGoogle Scholar
  21. 21.
    B. Li, J.D. Barrow, D.F. Mota, Phys. Rev. D 76, 044027 (2007) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    S.E. Perez Bergliaffa, Phys. Lett. B 642, 311 (2006) MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    J. Santos, J.S. Alcaniz, M.J. Reboucas, F.C. Carvalho, Phys. Rev. D 76, 083513 (2007) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, S. Zerbini, JCAP 0502, 010 (2005) MathSciNetADSGoogle Scholar
  25. 25.
    V. Faraoni, Phys. Rev. D 72, 061501 (2005) MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    V. Faraoni, S. Nadeau, Phys. Rev. D 72, 124005 (2005) ADSCrossRefGoogle Scholar
  27. 27.
    S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115 (2007) MATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    L.M. Sokolowski, Class. Quantum Gravity 24, 3391 (2007) MATHMathSciNetADSCrossRefGoogle Scholar
  29. 29.
    V. Faraoni, Phys. Rev. D 75, 067302 (2007) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    C.G. Böhmer, L. Hollenstein, F.S.N. Lobo, Phys. Rev. D 76, 084005 (2007) MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    S. Carloni, P.K.S. Dunsby, A. Troisi, Phys. Rev. D 77, 024024 (2008) MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    S. Capozziello, R. Cianci, C. Stornaiolo, S. Vignolo, Class. Quantum Gravity 24, 6417 (2007) MATHMathSciNetADSCrossRefGoogle Scholar
  33. 33.
    S. Nojiri, S.D. Odintsov, P.V. Tretyakov, Phys. Lett. B 651, 224 (2007) MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    S. Nojiri, S.D. Odintsov, Phys. Lett. B 652, 343 (2007) MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    S. Tsujikawa, Phys. Rev. D 77, 023507 (2008) MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    K.N. Ananda, S. Carloni, P.K.S. Dunsby, Phys. Rev. D 77, 024033 (2008) ADSCrossRefGoogle Scholar
  37. 37.
    A. Guarnizo, L. Castaneda, J.M. Tejeiro, arXiv:1002.0617v4 (2010)
  38. 38.
    T. Chiba, Phys. Lett. B 575, 1 (2003) MATHMathSciNetADSCrossRefGoogle Scholar
  39. 39.
    A.L. Erickcek, T.L. Smith, M. Kamionkowski, Phys. Rev. D 74, 121501 (2006) ADSCrossRefGoogle Scholar
  40. 40.
    T. Chiba, T.L. Smith, A.L. Erickcek, Phys. Rev. D 75, 124014 (2007) ADSCrossRefGoogle Scholar
  41. 41.
    S. Nojiri, S.D. Odintsov, Phys. Lett. B 659, 821 (2008) MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    S. Capozziello, A. Stabile, A. Troisi, Phys. Rev. D 76, 104019 (2007) MathSciNetADSCrossRefGoogle Scholar
  43. 43.
    S. Capozziello, A. Stabile, A. Troisi, Class. Quantum Gravity 25, 085004 (2008) MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    G.J. Olmo, Phys. Rev. D 75, 023511 (2007) MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    W. Hu, I. Sawicki, Phys. Rev. D 76, 064004 (2007) ADSCrossRefGoogle Scholar
  46. 46.
    S. Nojiri, S.D. Odintsov, Phys. Rev. D 68, 123512 (2003) MathSciNetADSCrossRefGoogle Scholar
  47. 47.
    V. Faraoni, Phys. Rev. D 74, 023529 (2006) MathSciNetADSCrossRefGoogle Scholar
  48. 48.
    T. Faulkner, M. Tegmark, E.F. Bunn, Y. Mao, Phys. Rev. D 76, 063505 (2007) MathSciNetADSCrossRefGoogle Scholar
  49. 49.
    P.J. Zhang, Phys. Rev. D 76, 024007 (2007) ADSCrossRefGoogle Scholar
  50. 50.
    C.S.J. Pun, Z. Kovacs, T. Harko, Phys. Rev. D 78, 024043 (2008) ADSCrossRefGoogle Scholar
  51. 51.
    I. Sawicki, W. Hu, Phys. Rev. D 75, 127502 (2007) MathSciNetADSCrossRefGoogle Scholar
  52. 52.
    L. Amendola, S. Tsujikawa, Phys. Lett. B 660, 125 (2008) ADSCrossRefGoogle Scholar
  53. 53.
    S. Nojiri, S.D. Odintsov, Phys. Lett.B 657, 238 (2007) MathSciNetADSCrossRefGoogle Scholar
  54. 54.
    S. Nojiri, S.D. Odintsov, Phys. Rev. D 77, 026007 (2008) MathSciNetADSCrossRefGoogle Scholar
  55. 55.
    G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Phys. Rev. D 77, 046009 (2008) ADSCrossRefGoogle Scholar
  56. 56.
    S. Nojiri, S.D. Odintsov, Talks given at the international conferences YKIS 2010, Gravitation and Cosmology (YITP, Kyoto) and QFTG-10 (Tomsk) (2010). arXiv:1008.4275
  57. 57.
    S. Capozziello, V.F. Cardone, A. Troisi, JCAP 0608, 001 (2006) ADSGoogle Scholar
  58. 58.
    S. Capozziello, V.F. Cardone, A. Troisi, Mon. Not. R. Astron. Soc. 375, 1423 (2007) ADSCrossRefGoogle Scholar
  59. 59.
    A. Borowiec, W. Godlowski, M. Szydlowski, Int. J. Geom. Methods Mod. Phys. 4, 183 (2007) MATHMathSciNetCrossRefGoogle Scholar
  60. 60.
    C.F. Martins, P. Salucci, Mon. Not. R. Astron. Soc. 381, 1103 (2007) ADSCrossRefGoogle Scholar
  61. 61.
    C.G. Boehmer, T. Harko, F.S.N. Lobo, Astropart. Phys. 29, 386 (2008) ADSCrossRefGoogle Scholar
  62. 62.
    C.G. Boehmer, T. Harko, F.S.N. Lobo, JCAP 03, 024 (2008) ADSGoogle Scholar
  63. 63.
    T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010) MathSciNetADSCrossRefGoogle Scholar
  64. 64.
    A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010) ADSGoogle Scholar
  65. 65.
    F.S.N. Lobo, arXiv:0807.1640 [gr-qc]
  66. 66.
    O. Bertolami, C.G. Boehmer, T. Harko, F.S.N. Lobo, Phys. Rev. D 75, 104016 (2007) MathSciNetADSCrossRefGoogle Scholar
  67. 67.
    T. Harko, Phys. Lett. B 669, 376 (2008) MathSciNetADSCrossRefGoogle Scholar
  68. 68.
    S. Nojiri, S.D. Odintsov, Phys. Lett. B 599, 137 (2004) MathSciNetADSCrossRefGoogle Scholar
  69. 69.
    G. Allemandi, A. Borowiec, M. Francaviglia, S.D. Odintsov, Phys. Rev. D 72, 063505 (2005) ADSCrossRefGoogle Scholar
  70. 70.
    O. Bertolami, J. Paramos, Phys. Rev. D 77, 084018 (2008) MathSciNetADSCrossRefGoogle Scholar
  71. 71.
    V. Faraoni, Phys. Rev. D 76, 127501 (2007) ADSCrossRefGoogle Scholar
  72. 72.
    T.P. Sotiriou, Phys. Lett. B 664, 225 (2008) MathSciNetADSCrossRefGoogle Scholar
  73. 73.
    O. Bertolami, J. Paramos, Class. Quantum Gravity 25, 245017 (2008) MathSciNetADSCrossRefGoogle Scholar
  74. 74.
    D. Puetzfeld, Y.N. Obukhov, Phys. Rev. D 78, 121501 (2008) MathSciNetADSCrossRefGoogle Scholar
  75. 75.
    O. Bertolami, T. Harko, F.S.N. Lobo, J. Paramos, arXiv:0811.2876 (2008)
  76. 76.
    T.P. Sotiriou, V. Faraoni, Class. Quantum Gravity 25, 205002 (2008) MathSciNetADSCrossRefGoogle Scholar
  77. 77.
    O. Bertolami, F.S.N. Lobo, J. Paramos, Phys. Rev. D 78, 064036 (2008) ADSCrossRefGoogle Scholar
  78. 78.
    V. Faraoni, Phys. Rev. D 80, 124040 (2009) MathSciNetADSCrossRefGoogle Scholar
  79. 79.
    O. Bertolami, M.C. Sequeira, Phys. Rev. D 79, 104010 (2009) MathSciNetADSCrossRefGoogle Scholar
  80. 80.
    S. Nesseris, Phys. Rev. D 79, 044015 (2009) ADSCrossRefGoogle Scholar
  81. 81.
    T. Harko, Phys. Rev. D 81, 084050 (2010) ADSCrossRefGoogle Scholar
  82. 82.
    T. Harko, F.S.N. Lobo, arXiv:1007.4415 (2010)
  83. 83.
    S. Thakur, A.A. Sen, T.R. Seshadri, arXiv:1007.5250 (2010)
  84. 84.
    T. Harko, Phys. Rev. D 81, 044021 (2010) ADSCrossRefGoogle Scholar
  85. 85.
    V. Faraoni, Cosmology in Scalar-Tensor Gravity (Kluwer Academic, Dordrecht, 2004) MATHGoogle Scholar
  86. 86.
    O. Bertolami. J. Páramos, S. Turyshev, General theory of relativity: Will it survive the next decade? gr-qc/0602016
  87. 87.
    O. Bertolami, F. Gil Pedro, M. Le Delliou, Phys. Lett. B 654, 165 (2007) ADSCrossRefGoogle Scholar
  88. 88.
    K. Bamba, S.D. Odintsov, JCAP 0804, 024 (2008) ADSGoogle Scholar
  89. 89.
    K. Bamba, S. Nojiri, S.D. Odintsov, Phys. Rev. D 77, 123532 (2008) ADSCrossRefGoogle Scholar
  90. 90.
    L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, Oxford, 1998) Google Scholar
  91. 91.
    T. Koivisto, Class. Quantum Gravity 23, 4289 (2006) MATHMathSciNetADSCrossRefGoogle Scholar
  92. 92.
    V. Fock, The Theory of Space, Time and Gravitation (Pergamon, London–New York–Paris–Los Angeles, 1959) MATHGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2010

Authors and Affiliations

  1. 1.Department of Physics and Center for Theoretical and Computational PhysicsThe University of Hong KongHong KongP.R. China
  2. 2.Centro de Astronomia e Astrofísica da Universidade de LisboaLisboaPortugal

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