Pathological behaviour of the scalar graviton in Hořava-Lifshitz gravity

Article

Abstract

We confirm the recent claims that, in the infrared limit of Hořava-Lifshitz gravity, the scalar graviton becomes a ghost if the sound speed squared is positive on the flat de Sitter and Minkowski background. In order to avoid the ghost and tame the instability, the sound speed squared should be negative and very small, which means that the flow parameter λ should be very close to its General Relativity (GR) value. We calculate the cubic interactions for the scalar graviton which are shown to have a similar structure with those of the curvature perturbation in k-inflation models. The higher order interactions become increasing important for a smaller sound speed squared, that is, when the theory approaches GR. This invalidates any linearized analysis and any predictability is lost in this limit as quantum corrections are not controllable. This pathological behaviour of the scalar graviton casts doubt on the validity of the projectable version of the theory.

Keywords

Models of Quantum Gravity Cosmology of Theories beyond the SM 

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]
    R.L. Arnowitt, S. Deser and C.W. Misner, Canonical variables for general relativity, Phys. Rev. 117 (1960) 1595 [SPIRES].MATHCrossRefMathSciNetADSGoogle Scholar
  3. [3]
    C. Charmousis, G. Niz, A. Padilla and P.M. Saffin, Strong coupling in Hořava gravity, JHEP 08 (2009) 070 [arXiv:0905.2579] [SPIRES].CrossRefADSGoogle Scholar
  4. [4]
    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
  5. [5]
    M. Li and Y. Pang, A Trouble with Hořava-Lifshitz Gravity, JHEP 08 (2009) 015 [arXiv:0905.2751] [SPIRES].ADSGoogle Scholar
  6. [6]
    P. Hořava, Membranes at Quantum Criticality, JHEP 03 (2009) 020 [arXiv:0812.4287] [SPIRES].ADSGoogle Scholar
  7. [7]
    A. Kobakhidze, On the infrared limit of Hořava’s gravity with the global Hamiltonian constraint, arXiv:0906.5401 [SPIRES].
  8. [8]
    D. Blas, O. Pujolàs and S. Sibiryakov, A healthy extension of Hořava gravity, arXiv:0909.3525 [SPIRES].
  9. [9]
    T.P. Sotiriou, M. Visser and S. Weinfurtner, Quantum gravity without Lorentz invariance, JHEP 10 (2009) 033 [arXiv:0905.2798] [SPIRES].CrossRefADSGoogle Scholar
  10. [10]
    J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP 05 (2003) 013 [astro-ph/0210603] [SPIRES].CrossRefADSGoogle Scholar
  11. [11]
    R.-G. Cai, B. Hu and H.-B. Zhang, Dynamical Scalar Degree of Freedom in Hořava-Lifshitz Gravity, Phys. Rev. D 80 (2009) 041501 [arXiv:0905.0255] [SPIRES].MathSciNetADSGoogle Scholar
  12. [12]
    J. Garriga, X. Montes, M. Sasaki and T. Tanaka, Canonical quantization of cosmological perturbations in the one-bubble open universe, Nucl. Phys. B 513 (1998) 343 [astro-ph/9706229] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    S. Mukohyama, Caustic avoidance in Hořava-Lifshitz gravity, JCAP 09 (2009) 005 [arXiv:0906.5069] [SPIRES].ADSGoogle Scholar
  14. [14]
    A. Wang and R. Maartens, Linear perturbations of cosmological models in the Hořava-Lifshitz theory of gravity without detailed balance, Phys. Rev. D 81 (2010) 024009 [arXiv:0907.1748] [SPIRES].ADSGoogle Scholar
  15. [15]
    C. Bogdanos and E.N. Saridakis, Perturbative instabilities in Hořava gravity, Class. Quant. Grav. 27 (2010) 075005 [arXiv:0907.1636] [SPIRES].CrossRefGoogle Scholar
  16. [16]
    S. Mukohyama, Dark matter as integration constant in Hořava-Lifshitz gravity, Phys. Rev. D 80 (2009) 064005 [arXiv:0905.3563] [SPIRES].ADSGoogle Scholar
  17. [17]
    D. Seery and J.E. Lidsey, Primordial non-Gaussianities in single field inflation, JCAP 06 (2005) 003 [astro-ph/0503692] [SPIRES].ADSGoogle Scholar
  18. [18]
    X. Chen, M.-x. Huang, S. Kachru and G. Shiu, Observational signatures and non-Gaussianities of general single field inflation, JCAP 01 (2007) 002 [hep-th/0605045] [SPIRES].ADSGoogle Scholar
  19. [19]
    F. Arroja and K. Koyama, Non-Gaussianity from the trispectrum in general single field inflation, Phys. Rev. D 77 (2008) 083517 [arXiv:0802.1167] [SPIRES].ADSGoogle Scholar
  20. [20]
    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
  21. [21]
    T. Kobayashi, Y. Urakawa and M. Yamaguchi, Large scale evolution of the curvature perturbation in Hořava-Lifshitz cosmology, JCAP 11 (2009) 015 [arXiv:0908.1005] [SPIRES].ADSGoogle Scholar
  22. [22]
    A. Wang, D. Wands and R. Maartens, Scalar field perturbations in Hořava-Lifshitz cosmology, arXiv:0909.5167 [SPIRES].
  23. [23]
    B. Chen, S. Pi and J.-Z. Tang, Power spectra of scalar and tensor modes in modified Hořava-Lifshitz gravity, arXiv:0910.0338 [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Institute of Cosmology and GravitationUniversity of PortsmouthPortsmouthU.K.
  2. 2.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan

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