de Sitter branes in a flat bulk of massive gravity

Abstract

We construct de Sitter branes in a flat bulk of massive gravity in 5D. We find two branches of solutions, reminiscent of the normal and self-accelerating branches in DGP, but with rather different properties. Neither branch has a self-accelerating limit: the background geometry requires having a nonvanishing tension. On the other hand, on both branches there are sub-branches where the leading order contributions of the tension to the curvature cancel. In these cases it turns out that larger tensions curve the background less. Further, both branches support a localized 4D massless graviton for a special choice of bulk mass terms. This choice may be protected by enhanced gauge symmetry. Finally, we generalize the solutions to the case of bigravity in a flat 5D bulk.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].

  2. [2]

    D.G. Boulware and S. Deser, Inconsistency of finite range gravitation, Phys. Lett. B 40 (1972) 227 [INSPIRE].

  3. [3]

    A. Higuchi, Forbidden Mass Range for Spin-2 Field Theory in de Sitter Space-time, Nucl. Phys. B 282 (1987) 397 [INSPIRE].

  4. [4]

    N. Arkani-Hamed, H. Georgi and M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys. 305 (2003) 96 [hep-th/0210184] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].

  6. [6]

    C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    S.F. Hassan and R.A. Rosen, Resolving the Ghost Problem in non-Linear Massive Gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].

  8. [8]

    S.F. Hassan and R.A. Rosen, Bimetric Gravity from Ghost-free Massive Gravity, JHEP 02 (2012) 126 [arXiv:1109.3515] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  9. [9]

    S.F. Hassan and R.A. Rosen, On Non-Linear Actions for Massive Gravity, JHEP 07 (2011) 009 [arXiv:1103.6055] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  10. [10]

    G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava and A.J. Tolley, Massive Cosmologies, Phys. Rev. D 84 (2011) 124046 [arXiv:1108.5231] [INSPIRE].

  11. [11]

    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].

    Article  Google Scholar 

  12. [12]

    D. Comelli, M. Crisostomi, F. Nesti and L. Pilo, FRW cosmology in ghost free massive gravity from bigravity, JHEP 03 (2012) 067 [Erratum JHEP 06 (2012) 020] [arXiv:1111.1983] [INSPIRE].

  13. [13]

    K. Koyama, G. Niz and G. Tasinato, Analytic solutions in non-linear massive gravity, Phys. Rev. Lett. 107 (2011) 131101 [arXiv:1103.4708] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  14. [14]

    K. Koyama, G. Niz and G. Tasinato, Strong interactions and exact solutions in non-linear massive gravity, Phys. Rev. D 84 (2011) 064033 [arXiv:1104.2143] [INSPIRE].

  15. [15]

    A. Nicolis and R. Rattazzi, Classical and quantum consistency of the DGP model, JHEP 06 (2004) 059 [hep-th/0404159] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  16. [16]

    C. Burrage, N. Kaloper and A. Padilla, Strong Coupling and Bounds on the Spin-2 Mass in Massive Gravity, Phys. Rev. Lett. 111 (2013) 021802 [arXiv:1211.6001] [INSPIRE].

  17. [17]

    N. Kaloper, A. Padilla, P. Saffin and D. Stefanyszyn, Unitarity and the Vainshtein Mechanism, Phys. Rev. D 91 (2015) 045017 [arXiv:1409.3243] [INSPIRE].

  18. [18]

    G. Gabadadze, Scale-up of Λ3 : Massive gravity with a higher strong interaction scale, Phys. Rev. D 96 (2017) 084018 [arXiv:1707.01739] [INSPIRE].

  19. [19]

    B. Bellazzini, F. Riva, J. Serra and F. Sgarlata, Beyond Positivity Bounds and the Fate of Massive Gravity, Phys. Rev. Lett. 120 (2018) 161101 [arXiv:1710.02539] [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    I.I. Kogan, S. Mouslopoulos and A. Papazoglou, The m → 0 limit for massive graviton in dS 4 and AdS 4 : How to circumvent the van Dam-Veltman-Zakharov discontinuity, Phys. Lett. B 503 (2001) 173 [hep-th/0011138] [INSPIRE].

  21. [21]

    M. Porrati, No van Dam-Veltman-Zakharov discontinuity in AdS space, Phys. Lett. B 498 (2001) 92 [hep-th/0011152] [INSPIRE].

  22. [22]

    A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  23. [23]

    G. Gabadadze and D. Pirtskhalava, Boundary Terms for Massive General Relativity, Phys. Rev. D 97 (2018) 124045 [arXiv:1803.11238] [INSPIRE].

  24. [24]

    T. Shiromizu, K.-i. Maeda and M. Sasaki, The Einstein equation on the 3-brane world, Phys. Rev. D 62 (2000) 024012 [gr-qc/9910076] [INSPIRE].

  25. [25]

    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, Inc., New York U.S.A. (1972) [INSPIRE].

  26. [26]

    N. Kaloper and A.D. Linde, Inflation and large internal dimensions, Phys. Rev. D 59 (1999) 101303 [hep-th/9811141] [INSPIRE].

  27. [27]

    N. Kaloper, Bent domain walls as brane worlds, Phys. Rev. D 60 (1999) 123506 [hep-th/9905210] [INSPIRE].

  28. [28]

    G.R. Dvali, G. Gabadadze and M. Porrati, 4 − D gravity on a brane in 5 − D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].

  29. [29]

    G.R. Dvali and G. Gabadadze, Gravity on a brane in infinite volume extra space, Phys. Rev. D 63 (2001) 065007 [hep-th/0008054] [INSPIRE].

  30. [30]

    C. Charmousis, R. Gregory, N. Kaloper and A. Padilla, DGP Specteroscopy, JHEP 10 (2006) 066 [hep-th/0604086] [INSPIRE].

  31. [31]

    R. Gregory, N. Kaloper, R.C. Myers and A. Padilla, A New perspective on DGP gravity, JHEP 10 (2007) 069 [arXiv:0707.2666] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  32. [32]

    C. Deffayet, Cosmology on a brane in Minkowski bulk, Phys. Lett. B 502 (2001) 199 [hep-th/0010186] [INSPIRE].

  33. [33]

    N. Arkani-Hamed, S. Dimopoulos, G. Dvali and G. Gabadadze, Nonlocal modification of gravity and the cosmological constant problem, hep-th/0209227 [INSPIRE].

  34. [34]

    G. Gabadadze, The Big Constant Out, The Small Constant In, Phys. Lett. B 739 (2014) 263 [arXiv:1406.6701] [INSPIRE].

  35. [35]

    N. Kaloper and A. Padilla, Sequestering the Standard Model Vacuum Energy, Phys. Rev. Lett. 112 (2014) 091304 [arXiv:1309.6562] [INSPIRE].

  36. [36]

    N. Kaloper and A. Padilla, Vacuum Energy Sequestering: The Framework and Its Cosmological Consequences, Phys. Rev. D 90 (2014) 084023 [Erratum ibid. D 90 (2014) 109901] [arXiv:1406.0711] [INSPIRE].

  37. [37]

    N. Kaloper, A. Padilla, D. Stefanyszyn and G. Zahariade, Manifestly Local Theory of Vacuum Energy Sequestering, Phys. Rev. Lett. 116 (2016) 051302 [arXiv:1505.01492] [INSPIRE].

  38. [38]

    N. Kaloper, Irrational Monodromies of Vacuum Energy, arXiv:1806.03308 [INSPIRE].

  39. [39]

    T. Gherghetta, M. Peloso and E. Poppitz, Emergent gravity from a mass deformation in warped spacetime, Phys. Rev. D 72 (2005) 104003 [hep-th/0507245] [INSPIRE].

  40. [40]

    B.K. El-Menoufi and L. Sorbo, Massless gravitons on a brane from massive gravity in five-dimensional Minkowski space, Phys. Rev. D 91 (2015) 064023 [arXiv:1411.5660] [INSPIRE].

  41. [41]

    N. Arkani-Hamed, S. Dimopoulos, N. Kaloper and R. Sundrum, A Small cosmological constant from a large extra dimension, Phys. Lett. B 480 (2000) 193 [hep-th/0001197] [INSPIRE].

  42. [42]

    S. Kachru, M.B. Schulz and E. Silverstein, Selftuning flat domain walls in 5 − D gravity and string theory, Phys. Rev. D 62 (2000) 045021 [hep-th/0001206] [INSPIRE].

  43. [43]

    G. Dvali and M.S. Turner, Dark energy as a modification of the Friedmann equation, astro-ph/0301510 [INSPIRE].

  44. [44]

    L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  45. [45]

    J. Garriga and T. Tanaka, Gravity in the brane world, Phys. Rev. Lett. 84 (2000) 2778 [hep-th/9911055] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  46. [46]

    I. Bengtsson, Note on massive spin-2 in curved space, J. Math. Phys. 36 (1995) 5805 [gr-qc/9411057] [INSPIRE].

  47. [47]

    S. Deser and A. Waldron, Stability of massive cosmological gravitons, Phys. Lett. B 508 (2001) 347 [hep-th/0103255] [INSPIRE].

  48. [48]

    M.A. Luty, M. Porrati and R. Rattazzi, Strong interactions and stability in the DGP model, JHEP 09 (2003) 029 [hep-th/0303116] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  49. [49]

    D. Gorbunov, K. Koyama and S. Sibiryakov, More on ghosts in DGP model, Phys. Rev. D 73 (2006) 044016 [hep-th/0512097] [INSPIRE].

  50. [50]

    E.G. Adelberger, B.R. Heckel and A.E. Nelson, Tests of the gravitational inverse square law, Ann. Rev. Nucl. Part. Sci. 53 (2003) 77 [hep-ph/0307284] [INSPIRE].

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Correspondence to James H. C. Scargill.

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Kaloper, N., Scargill, J.H.C. de Sitter branes in a flat bulk of massive gravity. J. High Energ. Phys. 2019, 132 (2019). https://doi.org/10.1007/JHEP03(2019)132

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Keywords

  • Classical Theories of Gravity
  • Field Theories in Higher Dimensions
  • Large Extra Dimensions