Renormalization Beyond the Decoupling Limit of Massive Gravity

  • Lavinia HeisenbergEmail author
Part of the Springer Theses book series (Springer Theses)


In this chapter we study the naturalness of the graviton mass and whether or not the specific structure of the graviton gets detuned in the full theory beyond the decoupling limit, and compare our conclusions to the estimations coming from the decoupling limit analysis. More concrete, we will address the two essential questions.


Decoupling Limit Massive Gravity Graviton Mass Vainshtein Mechanism Graviton Loops 
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  1. Berezhiani L, Chkareuli G, de Rham C, Gabadadze G, Tolley AJ (2012) On black holes in massive gravity. Phys Rev D 85:044024ADSCrossRefGoogle Scholar
  2. Buchbinder IL, de Berredo-Peixoto G, Shapiro IL (2007) Quantum effects in softly broken gauge theories in curved space-times. Phys Lett B 649:454–462. doi: 10.1016/j.physletb.2007.04.039
  3. Buchbinder IL, Pereira DD, Shapiro IL (2012) One-loop divergences in massive gravity theory. Phys Lett B 712:104–108. doi: 10.1016/j.physletb.2012.04.045
  4. Chamseddine AH, Mukhanov V (2011) Massive gravity simplified: a quadratic action. JHEP 1108:091MathSciNetADSCrossRefGoogle Scholar
  5. de Rham C, Gabadadze G (2010) Generalization of the Fierz-Pauli action. Phys Rev D 82:044020. doi: 10.1103/PhysRevD.82.044020
  6. de Rham C, Gabadadze G, Heisenberg L, Pirtskhalava D (2012) Non-renormalization and naturalness in a class of scalar-tensor theories. Phys Rev D 87:085017Google Scholar
  7. de Rham C, Gabadadze G, Tolley AJ (2011a) Helicity decomposition of ghost-free massive gravity. JHEP 1111:093. doi: 10.1007/JHEP11(2011)093
  8. de Rham C, Gabadadze G, Tolley AJ (2011b) Resummation of massive gravity. Phys Rev Lett 106:231101. doi: 10.1103/PhysRevLett.106.231101
  9. de Rham C, Heisenberg L, Ribeiro RH Quantum corrections in massive gravity at higher loop: mixing matter with gravitons (to appear)Google Scholar
  10. Deffayet C, Jacobson T (2012) On horizon structure of bimetric spacetimes. Class Quant Grav 29:065009. doi: 10.1088/0264-9381/29/6/065009
  11. Deffayet C, Mourad J, Zahariade G (2013) A note on ‘symmetric’ vielbeins in bimetric, massive, perturbative and non perturbative gravities. JHEP 1303:086Google Scholar
  12. Fasiello M, Tolley AJ (2013) Cosmological stability bound in massive gravity and bigravity. JCAP 1301:032Google Scholar
  13. Fierz M, Pauli W (1939) On relativistic wave equations for particles of arbitrary spin in an electromagnetic field. Proc Roy Soc Lond A 173:211–232MathSciNetADSCrossRefGoogle Scholar
  14. Gabadadze G, Hinterbichler K, Pirtskhalava D, Shang Y (2013) On the potential for general relativity and its geometry. Phys Rev D 88:084003Google Scholar
  15. Groot SN, Marco P, Matthew S (2007) Nonlinear properties of vielbein massive gravity. Eur Phys J C 51:741–752Google Scholar
  16. Hassan SF, Rosen RA (2011) On non-linear actions for massive gravity. JHEP 1107:009. doi: 10.1007/JHEP07(2011)009
  17. Hassan SF, Rosen RA (2012a) Bimetric gravity from ghost-free massive gravity. JHEP 1202:126. doi: 10.1007/JHEP02(2012)126
  18. Hassan SF, Rosen RA (2012b) Resolving the ghost problem in non-linear massive gravity. Phys Rev Lett 108:041101. 10.1103/PhysRevLett.108.041101
  19. Hinterbichler K, Rosen RA (2012) Interacting Spin-2 fields. JHEP 1207:047. doi: 10.1007/JHEP07(2012)047
  20. Koyama K, Niz G, Tasinato G (2011a) Analytic solutions in non-linear massive gravity. Phys Rev Lett 107:131101. doi: 10.1103/PhysRevLett.107.131101
  21. Koyama K, Niz G, Tasinato G (2011b) Strong interactions and exact solutions in non-linear massive gravity. Phys Rev D 84:064033. doi: 10.1103/PhysRevD.84.064033
  22. Nicolis A, Rattazzi R (2004) Classical and quantum consistency of the DGP model. JHEP 0406:059. doi: 10.1088/1126-6708/2004/06/059
  23. Ondo NA, Tolley AJ (2013) Complete decoupling limit of ghost-free massive gravity. JHEP 1311: 059Google Scholar
  24. Park M (2011) Quantum aspects of massive gravity. Class Quant Grav 28:105012ADSCrossRefGoogle Scholar
  25. ’t Hooft G, Veltman MJG (1974) One loop divergencies in the theory of gravitation. Ann Poincare Phys Theory A20:69–94Google Scholar
  26. Vainshtein AI (1972) To the problem of nonvanishing gravitation mass. Phys Lett B 39:393–394. doi: 10.1016/0370-2693(72)90147-5
  27. van Dam H, Veltman MJG (1970) Massive and massless Yang-Mills and gravitational fields. Nucl Phys B 22:397–411ADSCrossRefGoogle Scholar
  28. Zakharov VI (1970) Linearized gravitation theory and the graviton mass. JETP Lett 12:312ADSGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Royal Institute of TechnologyStockholmSweden

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