Avoiding Dark Energy with 1/R Modifications of Gravity

  • Richard Woodard
Part of the Lecture Notes in Physics book series (LNP, volume 720)

Abstract

Scalar quintessence seems epicyclic because one can choose the potential to reproduce any cosmology (I review the construction) and because the properties of this scalar seem to raise more questions than they answer. This is why there has been so much recent interest in modified gravity. I review the powerful theorem of Ostrogradski which demonstrates that the only potentially stable, local modification of general relativity is to make the Lagrangian an arbitrary function of the Ricci scalar. Such a theory can certainly reproduce the current phase of cosmic acceleration without Dark Energy. However, this explanation again seems epicyclic in that one can construct a function of the Ricci scalar to support any cosmology (I give the technique). Models of this form are also liable to problems in the way they couple to matter, both in terms of matter’s impact upon them and in terms of the long range gravitational force they predict. Because of these problems my own preference for avoiding Dark Energy is to bypass Ostrogradski’s theorem by considering the fully nonlocal effective action built up by quantum gravitational processes during the epoch of primordial inflation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.H. Cyburt, B.D. Fields and K.A. Olive, Phys. Lett. B 567, 227 (2003), astro-ph/0302431.Google Scholar
  2. 2.
    G. Bertone, D. Hooper and J. Silk, Phys. Rept. 405, 279 (2005), hep-ph/0404175.Google Scholar
  3. 3.
    M. Milgrom, Ap. J. 270, 365 (1983).CrossRefADSGoogle Scholar
  4. 4.
    R.H. Sanders and S.S. McGaugh, Ann. Rev. Astrophys 40, 263 (2002), astro-ph/0204521.Google Scholar
  5. 5.
    G. Gentile, P. Salucci, U. Klein, D. Vergani and P. Kalberla, Mon. Not. Roy. Astron. Soc. 351, 903 (2004), astro-ph/0403154.Google Scholar
  6. 6.
    J.D. Bekenstein, Phys. Rev. D 70, 083509 (2004), astro-ph/0403694.Google Scholar
  7. 7.
    C. Skordis, D.F. Mota, P.G. Ferreira and C. Boehm, Phys. Rev. Lett. 96, 011301 (2006), astro-ph/0505519.Google Scholar
  8. 8.
    R.A. Knop et al, Astrophys. J. 598, 102 (2003), astro-ph/0309368.Google Scholar
  9. 9.
    A.D. Reiss et al, Astrophys. J. 607, 665 (2004), astro-ph/0402512.Google Scholar
  10. 10.
    P. Astier et al, astro-ph/0510447.Google Scholar
  11. 11.
    D. Spergel et al, Astrophys. J. Suppl. 148, 175 (2003), astro-ph/0302209.Google Scholar
  12. 12.
    M. Tegmark et al, Phys. Rev. D 69, 103501 (2004), astro-ph/0310723.Google Scholar
  13. 13.
    C. Wetterich, Nucl. Phys. B 302, 668 (1988).CrossRefADSGoogle Scholar
  14. 14.
    B. Ratra and P.J.E. Peebles, Phys. Rev. D 37, 3406 (1988).CrossRefADSGoogle Scholar
  15. 15.
    N.C. Tsamis and R.P. Woodard, Ann. Phys. 267, 145 (1998), hep-th/9712331.Google Scholar
  16. 16.
    T.D. Saini, S. Raychaudhury, V. Saini and A.A. Starobinskiĭ, Phys. Rev. Lett. 85, 1162 (2000), astro-ph/9910231.Google Scholar
  17. 17.
    S. Capozziello, S. Nojiri and S.D. Odintsov, hep-th/0512118.Google Scholar
  18. 18.
    M. Ostrogradski, Mem. Ac. St. Petersbourg VI4, 385 (1850).Google Scholar
  19. 19.
    X. Jaén, J. Llosa and A. Molina, Phys. Rev. D 34, 2302 (1986).CrossRefADSGoogle Scholar
  20. 20.
    D.A. Eliezer and R.P. Woodard, Nucl. Phys. B 325, 389 (1989).CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    R.P. Woodard, Class. Quant. Grav. 10, 483 (1993).CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    N.C. Tsamis and R.P. Woodard, Phys. Rev. D 36, 3641 (1987).CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    K.S. Stelle Phys. Rev. D 16, 953 (1977).CrossRefADSMathSciNetGoogle Scholar
  24. 24.
    T.D. Lee and G.C. Wick Phys. Rev. D 2, 1033 (1970).CrossRefADSMathSciNetGoogle Scholar
  25. 25.
    N.C. Tsamis and R.P. Woodard, Ann. Phys. 168, 457 (1986).CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    S.W. Hawking and T. Hertog Phys. Rev. D 65, 103515 (2002), hep-th/0107088.Google Scholar
  27. 27.
    M.S. Plyushchay, Mod. Phys. Lett. A 4, 837 (1989).CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    D. Zoller, Phys. Rev. Lett. 65, 2236 (1990).CrossRefADSGoogle Scholar
  29. 29.
    R.P. Woodard, Phys. Lett. B 148, 440 (1984).CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    D.G. Boulware, G.T. Horowitz and A. Strominger Phys. Rev. Lett. 50, 1726 (1983).CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    A.A. Starobinskiĭ, Phys. Lett. B 91, 99 (1980).Google Scholar
  32. 32.
    A. Strominger, Phys. Rev. D 30, 2257 (1984).CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    G. Kleppe and R.P. Woodard, Nucl. Phys. B 388, 81 (1992).CrossRefADSGoogle Scholar
  34. 34.
    T.C. Cheng, P.M. Ho and M.C. Yeh, Nucl. Phys. B 625, 151 (2002), hep-th/0111160.Google Scholar
  35. 35.
    A. Jain and S.D. Joglekar, Int. J. Mod. Phys. A 19, 3409 (2004), hep-th/0307208.Google Scholar
  36. 36.
    D.J. Gross and A. Jevicki, Nucl. Phys. B 283, 1 (1987).CrossRefADSMathSciNetGoogle Scholar
  37. 37.
    D.J. Gross and A. Jevicki, Nucl. Phys. B 287, 225 (1987).CrossRefADSMathSciNetGoogle Scholar
  38. 38.
    D.J. Gross and A. Jevicki, Nucl. Phys. B 293, 29 (1987).CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    A. Konechny and A. Schwarz, Phys. Rept. 360, 353 (2002), hep-th0107251.Google Scholar
  40. 40.
    J.L. Hewett, F.J. Petriello and T.G. Rizzo, Phys. Rev. D 64, 075012 (2001), hep-ph/0010354.Google Scholar
  41. 41.
    D. Evens, J.W. Moffat, G. Kleppe and R.P. Woodard, Phys. Rev. D 43, 499 (1991).CrossRefADSGoogle Scholar
  42. 42.
    G. Kleppe and R.P. Woodard, Phys. Lett. B 253, 331 (1991).CrossRefADSGoogle Scholar
  43. 43.
    G. Kleppe and R.P. Woodard, Ann. Phys. B 221, 106 (1993).CrossRefADSGoogle Scholar
  44. 44.
    M.E. Soussa and R.P. Woodard, Class. Quant. Grav. 20, 2737 (2003), astro-ph/0302030.Google Scholar
  45. 45.
    T. Biswas, A. Mazumdar and W. Siegel, JCAP 0603, 009 (2006), hep-th/0508194.Google Scholar
  46. 46.
    R.P. Woodard, Phys. Rev. A 62, 052105 (2000), hep-th/0006207.Google Scholar
  47. 47.
    J. Llosa, hep-th/0201087.Google Scholar
  48. 48.
    R.P. Woodard, Phys. Rev. A 67, 016102 (2003), hep-th/0207191.Google Scholar
  49. 49.
    A.O. Barvinsky, Y.V. Gusev, G.A. Vilkovisky and V.V. Zhytnikov, J. Math. Phys. 35, 3525 (1994), gr-qc/9404061.Google Scholar
  50. 50.
    A.O. Barvinsky and V.F. Mukhanov, Phys. Rev. D 66, 065007 (2202), hep-th/0203132.Google Scholar
  51. 51.
    D.L. Bennett, H.B. Nielsen and R.P. Woodard, Phys. Rev. D 57, 1167 (1998, hep-th/9707088.Google Scholar
  52. 52.
    S. Nojiri and S.D. Odintsov, Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007), hep-th/0601213.Google Scholar
  53. 53.
    S.M. Carroll, V. Duvvuri, M. Trodden and M.S. Turner, Phys. Rev. D 70, 043528 (2004), astro-ph/0306438.Google Scholar
  54. 54.
    S. Capozziello, S. Carloni and A. Troisi, Phys. Rev. D 70, 043528 (2004), astro-ph/0306438.Google Scholar
  55. 55.
    S.M. Carroll, A. De Felice, V. Duvvuri, D.A. Easson, M. Trodden and M.S. Turner, Phys. Rev. D 71, 063513 (2005), astro-ph/0410031.Google Scholar
  56. 56.
    S. Nojiri and S.D. Odintsov, Phys. Lett. B 576, 5 (2003), hep-th/0307071.Google Scholar
  57. 57.
    A.D. Dolgov and M. Kawasaki, Phys. Let. B 573, 1 (2003), astro-ph/0307285.Google Scholar
  58. 58.
    R. Dick, Gen. Rel. Grav. 36, 217 (2004), gr-qc/0307052.Google Scholar
  59. 59.
    S. Nojiri and S.D. Odintsov, Phys. Rev. D 68, 123512 (2003), hep-th/0307288.Google Scholar
  60. 60.
    M.E. Soussa and R.P. Woodard, Gen. Rel. Grav. 36, 855 (2004), astro-ph/0308114.Google Scholar
  61. 61.
    S. Nojiri and S.D. Odintsov, Gen. Rel. Grav. 36, 1765 (2004), hep-th/0308176.Google Scholar
  62. 62.
    M. Amarzguioui, Ø. Elgaroy, D.F. Mota and T. Multamäki, astro-ph/0510519.Google Scholar
  63. 63.
    D. Espriu, T. Multamäki and E.C. Vagenas, Phys. Lett. B 628, 197 (2005), gr-qc/0503033.Google Scholar
  64. 64.
    N.C. Tsamis and R.P. Woodard, Ann. Phys. 238, 1 (1995).CrossRefADSMathSciNetGoogle Scholar
  65. 65.
    P. Martineau and R. Brandenberger, astro-ph/0510523.Google Scholar
  66. 66.
    N.C. Tsamis and R.P. Woodard, Nucl. Phys. B 474, 235 (1996), hep-ph/9602315.Google Scholar
  67. 67.
    N.C. Tsamis and R.P. Woodard, Ann. Phys. 253, 1 (1997), hep-ph/9602317.Google Scholar
  68. 68.
    V.K. Onemli and R.P. Woodard, Class. Quant. Grav. 19, 4607 (2002), gr-qc/0204065.Google Scholar
  69. 69.
    V.K. Onemli and R.P. Woodard, Phys. Rev. D 70, 107301 (2004), gr-qc/0406098.Google Scholar
  70. 70.
    A.A. Starobinskiĭ, Stochastic de Sitter (inflationary) stage in the early universe. In, Field Theory, Quantum Gravity and Strings, ed by H.J. de Vega and N. Sanchez (Springer-Verlag, Berlin, 1986) pp 107–126.Google Scholar
  71. 71.
    A.A. Starobinskiĭ and J.Yokoyama, Phys. Rev. D 50, 6357 (1994), astro-ph/-9407016.Google Scholar
  72. 72.
    R.P. Woodard, Nucl. Phys. Proc. Suppl. 148, 108 (2005), astro-ph/0502556.Google Scholar
  73. 73.
    N.C. Tsamis and R.P. Woodard, Nucl. Phys. B 724, 295 (2005), gr-qc/0505115.Google Scholar
  74. 74.
    M.E. Soussa and R.P. Woodard, Phys. Lett. B 578, 253 (2004), astro-ph/0307358.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Richard Woodard
    • 1
  1. 1.Department of PhysicsUniversity of FloridaGainesvilleUSA

Personalised recommendations