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Extended DBI massive gravity with generalized fiducial metric

  • Tossaporn Chullaphan
  • Lunchakorn Tannukij
  • Pitayuth Wongjun
Open Access
Regular Article - Theoretical Physics

Abstract

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.

Keywords

Classical Theories of Gravity Cosmology of Theories beyond the SM 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    H. van Dam and M.J.G. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys. B 22 (1970) 397 [INSPIRE].ADSGoogle Scholar
  3. [3]
    V.I. Zakharov, Linearized gravitation theory and the graviton mass, JETP Lett. 12 (1970) 312 [Pisma Zh. Eksp. Teor. Fiz. 12 (1970) 447] [INSPIRE].
  4. [4]
    A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].ADSGoogle Scholar
  6. [6]
    C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].ADSGoogle Scholar
  7. [7]
    C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    G. D’Amico et al., Massive cosmologies, Phys. Rev. D 84 (2011) 124046 [arXiv:1108.5231] [INSPIRE].ADSGoogle Scholar
  9. [9]
    A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Open FRW universes and self-acceleration from nonlinear massive gravity, JCAP 11 (2011) 030 [arXiv:1109.3845] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    M. Fasiello and A.J. Tolley, Cosmological perturbations in Massive Gravity and the Higuchi bound, JCAP 11 (2012) 035 [arXiv:1206.3852] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    D. Langlois and A. Naruko, Cosmological solutions of massive gravity on de Sitter, Class. Quant. Grav. 29 (2012) 202001 [arXiv:1206.6810] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    D. Langlois and A. Naruko, Bouncing cosmologies in massive gravity on de Sitter, Class. Quant. Grav. 30 (2013) 205012 [arXiv:1305.6346] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Cosmological perturbations of self-accelerating universe in nonlinear massive gravity, JCAP 03 (2012) 006 [arXiv:1111.4107] [INSPIRE].CrossRefGoogle Scholar
  14. [14]
    A. De Felice, A.E. Gumrukcuoglu and S. Mukohyama, Massive gravity: nonlinear instability of the homogeneous and isotropic universe, Phys. Rev. Lett. 109 (2012) 171101 [arXiv:1206.2080] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Anisotropic Friedmann-Robertson-Walker universe from nonlinear massive gravity, Phys. Lett. B 717 (2012) 295 [arXiv:1206.2723] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    A. De Felice, A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Nonlinear stability of cosmological solutions in massive gravity, JCAP 05 (2013) 035 [arXiv:1303.4154] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Q.-G. Huang, Y.-S. Piao and S.-Y. Zhou, Mass-varying massive gravity, Phys. Rev. D 86 (2012) 124014 [arXiv:1206.5678] [INSPIRE].ADSGoogle Scholar
  18. [18]
    G. D’Amico, G. Gabadadze, L. Hui and D. Pirtskhalava, Quasidilaton: theory and cosmology, Phys. Rev. D 87 (2013) 064037 [arXiv:1206.4253] [INSPIRE].ADSzbMATHGoogle Scholar
  19. [19]
    A.E. Gumrukcuoglu, K. Hinterbichler, C. Lin, S. Mukohyama and M. Trodden, Cosmological perturbations in extended massive gravity, Phys. Rev. D 88 (2013) 024023 [arXiv:1304.0449] [INSPIRE].ADSGoogle Scholar
  20. [20]
    G. D’Amico, G. Gabadadze, L. Hui and D. Pirtskhalava, On cosmological perturbations of quasidilaton, Class. Quant. Grav. 30 (2013) 184005 [arXiv:1304.0723] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    A. De Felice and S. Mukohyama, Towards consistent extension of quasidilaton massive gravity, Phys. Lett. B 728 (2014) 622 [arXiv:1306.5502] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    A. De Felice, A.E. Gumrukcuoglu and S. Mukohyama, Generalized quasidilaton theory, Phys. Rev. D 88 (2013) 124006 [arXiv:1309.3162] [INSPIRE].ADSGoogle Scholar
  23. [23]
    L. Heisenberg, Revisiting perturbations in extended quasidilaton massive gravity, JCAP 04 (2015) 010 [arXiv:1501.07796] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    T. Kahniashvili et al., Cosmic expansion in extended quasidilaton massive gravity, Phys. Rev. D 91 (2015) 041301 [arXiv:1412.4300] [INSPIRE].ADSGoogle Scholar
  25. [25]
    A.E. Gumrukcuoglu, L. Heisenberg and S. Mukohyama, Cosmological perturbations in massive gravity with doubly coupled matter, JCAP 02 (2015) 022 [arXiv:1409.7260] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    A.R. Solomon et al., Cosmological viability of massive gravity with generalized matter coupling, JCAP 04 (2015) 027 [arXiv:1409.8300] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    K. Hinterbichler, J. Stokes and M. Trodden, Cosmologies of extended massive gravity, Phys. Lett. B 725 (2013) 1 [arXiv:1301.4993] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    G. Gabadadze, K. Hinterbichler, J. Khoury, D. Pirtskhalava and M. Trodden, A covariant master theory for novel galilean invariant models and massive gravity, Phys. Rev. D 86 (2012) 124004 [arXiv:1208.5773] [INSPIRE].ADSGoogle Scholar
  29. [29]
    M. Andrews, K. Hinterbichler, J. Stokes and M. Trodden, Cosmological perturbations of massive gravity coupled to DBI galileons, Class. Quant. Grav. 30 (2013) 184006 [arXiv:1306.5743] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    S. Mukohyama, T. Shiromizu and K.-i. Maeda, Global structure of exact cosmological solutions in the brane world, Phys. Rev. D 62 (2000) 024028 [hep-th/9912287] [INSPIRE].ADSMathSciNetGoogle Scholar
  31. [31]
    S.F. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free massive gravity with a general reference metric, JHEP 02 (2012) 026 [arXiv:1109.3230] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    M. Andrews, G. Goon, K. Hinterbichler, J. Stokes and M. Trodden, Massive gravity coupled to galileons is ghost-free, Phys. Rev. Lett. 111 (2013) 061107 [arXiv:1303.1177] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Tossaporn Chullaphan
    • 1
    • 2
  • Lunchakorn Tannukij
    • 3
  • Pitayuth Wongjun
    • 1
    • 4
  1. 1.The Institute for Fundamental StudyNaresuan UniversityPhitsanulokThailand
  2. 2.Department of Physics, Faculty of ScienceUdon Thani Rajabhat UniversityUdon ThaniThailand
  3. 3.Department of Physics, Faculty of ScienceMahidol UniversityBangkokThailand
  4. 4.Thailand Center of Excellence in PhysicsMinistry of EducationBangkokThailand

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