Lessons from the decoupling limit of Hořava gravity

Article

Abstract

We consider the so-called “healthy” extension of Hořava gravity in the limit where the Stuckelberg field decouples from the graviton. We verify the alleged strong coupling problem in this limit, under the assumption that no large dimensionless parameters are put in by hand. This follows from the fact that the dispersion relation for the Stuckelberg field does not have the desired z = 3 anisotropic scaling in the UV. To get the desired scaling and avoid strong coupling one has to introduce a low scale of Lorentz violation and retain some coupling between the graviton and the Stuckelberg field. We also make use of the foliation preserving symmetry to show how the Stuckelberg field couples to some violation of energy conservation. We source the Stuckelberg field using a point particle with a slowly varying mass and show that two such particles feel a constant attractive force. In this particular example, we see no Vainshtein effect, and violations of the Equivalence Principle. The latter is probably generic to other types of source and could potentially be used to place lower bounds on the scale of Lorentz violation.

Keywords

Models of Quantum Gravity Classical Theories of Gravity 

References

  1. [1]
    P. Hořava, Quantum Gravity at a Lifshitz Point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [SPIRES].ADSGoogle Scholar
  2. [2]
    P. Hořava, Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point, Phys. Rev. Lett. 102 (2009) 161301 [arXiv:0902.3657] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  3. [3]
    K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [SPIRES].MathSciNetADSGoogle Scholar
  4. [4]
    A. Pais and G.E. Uhlenbeck, On Field theories with nonlocalized action, Phys. Rev. 79 (1950) 145 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  5. [5]
    J.M. Cline, S. Jeon and G.D. Moore, The phantom menaced: Constraints on low-energy effective ghosts, Phys. Rev. D 70 (2004) 043543 [hep-ph/0311312] [SPIRES].ADSGoogle Scholar
  6. [6]
    C. Charmousis, G. Niz, A. Padilla and P.M. Saffin, Strong coupling in Hořava gravity, JHEP 08 (2009) 070 [arXiv:0905.2579] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  7. [7]
    D. Blas, O. Pujolàs and S. Sibiryakov, On the Extra Mode and Inconsistency of Hořava Gravity, JHEP 10 (2009) 029 [arXiv:0906.3046] [SPIRES].CrossRefADSGoogle Scholar
  8. [8]
    D. Blas, O. Pujolàs and S. Sibiryakov, Consistent Extension of Hořava Gravity, Phys. Rev. Lett. 104 (2010) 181302 [arXiv:0909.3525] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    A. Papazoglou and T.P. Sotiriou, Strong coupling in extended Hořava-Lifshitz gravity, Phys. Lett. B 685 (2010) 197 [arXiv:0911.1299] [SPIRES].MathSciNetADSGoogle Scholar
  10. [10]
    D. Blas, O. Pujolàs and S. Sibiryakov, Comment on ‘Strong coupling in extended Hořava-Lifshitz gravity’, Phys. Lett. B 688 (2010) 350 [arXiv:0912.0550] [SPIRES].ADSGoogle Scholar
  11. [11]
    C. Germani, A. Kehagias and K. Sfetsos, Relativistic Quantum Gravity at a Lifshitz Point, JHEP 09 (2009) 060 [arXiv:0906.1201] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  12. [12]
    C. Bogdanos and E.N. Saridakis, Perturbative instabilities in Hořava gravity, Class. Quant. Grav. 27 (2010) 075005 [arXiv:0907.1636] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    K. Koyama and F. Arroja, Pathological behaviour of the scalar graviton in Hořava-Lifshitz gravity, JHEP 03 (2010) 061 [arXiv:0910.1998] [SPIRES].CrossRefGoogle Scholar
  14. [14]
    Y. Huang, A. Wang and Q. Wu, Stability of the de Sitter spacetime in Hořava-Lifshitz theory, arXiv:1003.2003 [SPIRES].
  15. [15]
    T.P. Sotiriou, M. Visser and S. Weinfurtner, Phenomenologically viable Lorentz-violating quantum gravity, Phys. Rev. Lett. 102 (2009) 251601 [arXiv:0904.4464] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    G. Dvali, Predictive Power of Strong Coupling in Theories with Large Distance Modified Gravity, New J. Phys. 8 (2006) 326 [hep-th/0610013] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [SPIRES].ADSGoogle Scholar
  18. [18]
    G.R. Dvali, G. Gabadadze and M. Porrati, 4D gravity on a brane in 5D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [SPIRES].MathSciNetADSGoogle Scholar
  19. [19]
    C. Charmousis, R. Gregory, N. Kaloper and A. Padilla, DGP specteroscopy, JHEP 10 (2006) 066 [hep-th/0604086] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  20. [20]
    A. Padilla, A short review of ‘DGP Specteroscopy’, J. Phys. A 40 (2007) 6827 [hep-th/0610093] [SPIRES].ADSGoogle Scholar
  21. [21]
    D. Gorbunov, K. Koyama and S. Sibiryakov, More on ghosts in DGP model, Phys. Rev. D 73 (2006) 044016 [hep-th/0512097] [SPIRES].ADSGoogle Scholar
  22. [22]
    R. Gregory, N. Kaloper, R.C. Myers and A. Padilla, A New Perspective on DGP Gravity, JHEP 10 (2007) 069 [arXiv:0707.2666] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  23. [23]
    M.A. Luty, M. Porrati and R. Rattazzi, Strong interactions and stability in the DGP model, JHEP 09 (2003) 029 [hep-th/0303116] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    A. Nicolis and R. Rattazzi, Classical and quantum consistency of the DGP model, JHEP 06 (2004) 059 [hep-th/0404159] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    C. Deffayet, G.R. Dvali, G. Gabadadze and A.I. Vainshtein, Nonperturbative continuity in graviton mass versus perturbative discontinuity, Phys. Rev. D 65 (2002) 044026 [hep-th/0106001] [SPIRES].ADSGoogle Scholar
  26. [26]
    M. Visser, Lorentz symmetry breaking as a quantum field theory regulator, Phys. Rev. D 80 (2009) 025011 [arXiv:0902.0590] [SPIRES].MathSciNetADSGoogle Scholar
  27. [27]
    M. Visser, Power-counting renormalizability of generalized Hořava gravity, arXiv:0912.4757 [SPIRES].
  28. [28]
    R.A. Hulse and J.H. Taylor, Discovery of a pulsar in a binary system, Astrophys. J. 195 (1975) L51 [SPIRES].CrossRefADSGoogle Scholar
  29. [29]
    E. Berti, A. Buonanno and C.M. Will, Estimating spinning binary parameters and testing alternative theories of gravity with LISA, Phys. Rev. D 71 (2005) 084025 [gr-qc/0411129] [SPIRES].ADSGoogle Scholar
  30. [30]
    C.M. Will and H.W. Zaglauer, Gravitational radiation, close binary systems, and the Brans-Dicke theory of gravity, Astrophys. J. 346 (1989) 366 [SPIRES].CrossRefADSGoogle Scholar
  31. [31]
    S. Schlamminger, K.Y. Choi, T.A. Wagner, J.H. Gundlach and E.G. Adelberger, Test of the Equivalence Principle Using a Rotating Torsion Balance, Phys. Rev. Lett. 100 (2008) 041101 [arXiv:0712.0607] [SPIRES].CrossRefADSGoogle Scholar
  32. [32]
    S. Baessler et al., Improved Test of the Equivalence Principle for Gravitational Self-Energy, Phys. Rev. Lett. 83 (1999) 3585 [SPIRES].CrossRefADSGoogle Scholar
  33. [33]
    M. Li and Y. Pang, A Trouble with Hořava-Lifshitz Gravity, JHEP 08 (2009) 015 [arXiv:0905.2751] [SPIRES].MathSciNetADSGoogle Scholar
  34. [34]
    M. Henneaux, A. Kleinschmidt and G.L. Gomez, A dynamical inconsistency of Hořava gravity, Phys. Rev. D 81 (2010) 064002 [arXiv:0912.0399] [SPIRES].ADSGoogle Scholar
  35. [35]
    J. Kluson, Note About Hamiltonian Formalism of Modified F(R) Hořava-Lifshitz Gravities and Their Healthy Extension, arXiv:1002.4859 [SPIRES].
  36. [36]
    J.M. Pons and P. Talavera, Remarks on the consistency of minimal deviations from General Relativity, arXiv:1003.3811 [SPIRES].
  37. [37]
    R. Iengo, J.G. Russo and M. Serone, Renormalization group in Lifshitz-type theories, JHEP 11 (2009) 020 [arXiv:0906.3477] [SPIRES].CrossRefADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.School of Physics and AstronomyUniversity of NottinghamNottinghamU.K.

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