Abstract
Physics studies Nature, its matter content and its evolution modeled by the laws of physics.
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Notes
- 1.
In fact, it must be included from an effective field theory point of view.
- 2.
One can basically use the mass term, the coupling to matter or the kinetic term of the scalar field in order to achieve screening.
- 3.
The non-linear extension for the spin-1 field is trivial in the sense that one does not have to deal with the Boulware-Deser ghost.
- 4.
Note that we are neglecting the helicity-1 field in \({\upvarphi }^a\) since at linear order this field decouples completely. If we had included the helicity-1 field in the expansion of \({\upvarphi }^\mathrm {a}=(x^{\upalpha }+\mathrm {A}^{\upalpha }-{\uppi }^{\upalpha })\, {\updelta }^\mathrm {a}_{\upalpha }\) then the expression for the covariant tensor would have contained the contribution of that field as well \(\mathrm {H}_{{\upmu }{\upnu }}=\frac{\mathrm {h}_{{\upmu }{\upnu }}}{\mathrm {M}_\mathrm{Pl}}+\partial _{\upmu }\mathrm {A}_{\upnu }+\partial _{\upnu }\mathrm {A}_{\upmu }+\partial _{\upmu }{\uppi }_{\upnu }+ \partial _{\upnu }{\uppi }_{\upmu }+\cdots \).
- 5.
In general, there is also a tadpole contribution \(\mathcal {L}_1\), that depends on the bulk content.
References
Arkani-Hamed N, Dimopoulos S, Dvali G, Gabadadze G (2002) Nonlocal modification of gravity and the cosmological constant problem
Arkani-Hamed N, Georgi H, Schwartz MD (2003) Effective field theory for massive gravitons and gravity in theory space. Ann Phys 305:96–118. doi:10.1016/S0003-4916(03)00068-X
Babichev E, Deffayet C, Ziour R (2009) K-Mouflage gravity. Int J Mod Phys D18:2147–2154. doi:10.1142/S0218271809016107
Bergshoeff EA, Hohm O, Townsend PK (2009) Massive gravity in three dimensions. Phys Rev Lett 102:201301. doi:10.1103/PhysRevLett.102.201301
Boehmer CG, Harko T (2007) Dark energy as a massive vector field. Eur Phys J C 50:423–429. doi:10.1140/epjc/s10052-007-0210-1
Burgess CP (2007) Introduction to effective field theory. Ann Rev Nucl Part Sci 57:329–362. doi:10.1146/annurev.nucl.56.080805.140508
Burrage C, de Rham C, Heisenberg L (2011) de Sitter Galileon. JCAP 1105:025. doi:10.1088/1475-7516/2011/05/025
Burrage C, de Rham C, Seery D, Tolley AJ (2011) Galileon inflation. JCAP 1101:014. doi:10.1088/1475-7516/2011/01/014
Chkareuli G, Pirtskhalava D (2012) Vainshtein mechanism in \(\Lambda _3\)—theories. Phys Lett B 713:99–103. doi:10.1016/j.physletb.2012.05.030
Chow N, Khoury J (2009) Galileon cosmology. Phys Rev D 80:024037. doi:10.1103/PhysRevD.80.024037
Christos C, Ruth G, Nemanja K, Antonio P (2006) DGP Specteroscopy. JHEP 0610:066. doi:10.1088/1126-6708/2006/10/066
Creminelli P, Nicolis A, Trincherini E (2010) Galilean genesis: an alternative to inflation. JCAP 1011:021. doi:10.1088/1475-7516/2010/11/021
Davis SC (2003) Generalized Israel junction conditions for a Gauss-Bonnet brane world. Phys Rev D 67:024030. doi:10.1103/PhysRevD.67.024030
de Fromont P, de Rham C, Heisenberg L, Matas A (2013) Superluminality in the Bi- and Multi-Galileon. JHEP 1307:067. doi:10.1007/JHEP07(2013)067
de Rham C (2010) Massive gravity from Dirichlet boundary conditions. Phys Lett B 688:137–141
de Rham C, Dvali G, Hofmann S, Khoury J, Pujolas O et al (2008) Cascading gravity: extending the Dvali-Gabadadze-Porrati model to higher dimension. Phys Rev Lett 100:251603. doi:10.1103/PhysRevLett.100.251603
de Rham C, Gabadadze G (2010a) Selftuned massive spin-2. Phys Lett B 693:334–338. doi:10.1016/j.physletb.2010.08.043
de Rham C, Gabadadze G (2010b) Generalization of the Fierz-Pauli action. Phys Rev D 82:044020. doi:10.1103/PhysRevD.82.044020
de Rham C, Gabadadze G, Heisenberg L, Pirtskhalava D (2011) Cosmic acceleration and the helicity-0 graviton. Phys Rev D 83:103516. doi:10.1103/PhysRevD.83.103516
de Rham C, Gabadadze G, Heisenberg L, Pirtskhalava D (2012) Non-renormalization and naturalness in a class of scalar-tensor theories. Phys Rev D 87:085017
de Rham C, Gabadadze G, Pirtskhalava D, Tolley AJ, Yavin I (2011) Nonlinear dynamics of 3D massive gravity. JHEP 1106:028. doi:10.1007/JHEP06(2011)028
de Rham C, Gabadadze G, Tolley AJ (2011) Resummation of massive gravity. Phys Rev Lett 106:231101. doi:10.1103/PhysRevLett.106.231101
de Rham C, Heisenberg L (2011) Cosmology of the galileon from massive gravity. Phys Rev D 84:043503. doi:10.1103/PhysRevD.84.043503
de Rham C, Heisenberg L, Ribeiro RH (2015) Quantum corrections in massive gravity at higher loop: mixing matter with gravitons to appear
de Rham C, Tolley AJ (2006) Mimicking Lambda with a spin-two ghost condensate. JCAP 0607:004. doi:10.1088/1475-7516/2006/07/004
de Rham C, Tolley A (2010) DBI and the Galileon reunited. JCAP 1005:015. doi:10.1088/1475-7516/2010/05/015
Deffayet C, Dvali GR, Gabadadze G (2002) Accelerated universe from gravity leaking to extra dimensions. Phys Rev D 65: 044023. doi:10.1103/PhysRevD.65.044023
Deffayet C, Dvali GR, Gabadadze G, Vainshtein AI (2002) Nonperturbative continuity in graviton mass versus perturbative discontinuity. Phys Rev D 65:044026. doi:10.1103/PhysRevD.65.044026
Deffayet C, Esposito-Farese G, Vikman A (2009) Covariant galileon. Phys Rev D 79:084003. doi:10.1103/PhysRevD.79.084003
Deffayet C, Pujolas O, Sawicki I, Vikman A (2010) Imperfect dark energy from kinetic gravity braiding. JCAP 1010:026. doi:10.1088/1475-7516/2010/10/026
Doran M, Lilley MJ, Schwindt J, Wetterich C (2001) Quintessence and the separation of CMB peaks. Astrophys J 559:501–506. doi:10.1086/322253
Dvali GR, Gabadadze G, Porrati M (2000) 4-D gravity on a brane in 5-D Minkowski space. Phys Lett B485:208–214. doi:10.1016/S0370-2693(00)00669-9
Dvali G, Gabadadze G, Shifman M (2002) Diluting cosmological constant via large distance modification of gravity. World Scientific, Singapore, pp 566–581
Dvali G, Gabadadze G, Shifman M (2003) Diluting cosmological constant in infinite volume extra dimensions. Phys Rev D 67:044020. doi:10.1103/PhysRevD.67.044020
Dvali G, Hofmann S, Khoury J (2007) Degravitation of the cosmological constant and graviton width. Phys Rev D 76:084006. doi:10.1103/PhysRevD.76.084006
Fairlie D (2011) Comments on galileons. J Phys A44:305201. doi:10.1088/1751-8113/44/30/305201
Fairlie DB, Govaerts J, Morozov A (1992) Universal field equations with covariant solutions. Nucl Phys B 373:214–232. doi:10.1016/0550-3213(92)90455-K
Fasiello M, Tolley AJ (2013) Cosmological stability bound in massive gravity and bigravity
Fierz M, Pauli W (1939) On relativistic wave equations for particles of arbitrary spin in an electromagnetic field. Proc Roy Soc Lond A173:211–232
Gabadadze G (2009) General relativity with an auxiliary dimension. Phys Lett B 681:89–95
Gabadadze G, Shifman M (2004) Softly massive gravity. Phys Rev D 69:124032. doi:10.1103/PhysRevD.69.124032
Golovnev A, Mukhanov V, Vanchurin V (2008) Vector inflation. JCAP 0806:009. doi:10.1088/1475-7516/2008/06/009
Goon G, Hinterbichler K, Trodden M (2011) Symmetries for Galileons and DBI scalars on curved space. JCAP 1107:017. doi:10.1088/1475-7516/2011/07/017
Hassan SF, Rosen RA (2011) On non-linear actions for massive gravity. JHEP 1107:009. doi:10.1007/JHEP07(2011)009
Hassan SF, Rosen RA (2012) Bimetric gravity from ghost-free massive gravity. JHEP 1202:126. doi:10.1007/JHEP02(2012)126
Hassan SF, Schmidt-May A, von Strauss M (2012) Metric formulation of ghost-free multivielbein theory
Hinterbichler K, Nicolis A, Porrati M (2009) Superluminality in DGP. JHEP 0909:089. doi:10.1088/1126-6708/2009/09/089
Hinterbichler K, Khoury J (2010) Symmetron fields: screening long-range forces through local symmetry restoration. Phys Rev Lett 104:231301. doi:10.1103/PhysRevLett.104.231301
Hinterbichler K, Khoury J (2012) The pseudo-conformal universe: scale invariance from spontaneous breaking of conformal symmetry. JCAP 1204:023. doi:10.1088/1475-7516/2012/04/023
Hinterbichler K, Rosen RA (2012) Interacting spin-2 fields. JHEP 1207:047. doi:10.1007/JHEP07(2012)047
Jiménez JB, Durrer R, Heisenberg L, Thorsrud M (2013) Stability of Horndeski vector-tensor interactions. JCAP 1310:064. doi:10.1088/1475-7516/2013/10/064
Jimenez JB, Froes ALD, Mota DF (2013) Screening vector field modifications of general relativity. Phys Lett B 725:212–217. doi:10.1016/j.physletb.2013.07.032
Khoury J, Weltman A (2004) Chameleon cosmology. Phys Rev D 69:044026. doi:10.1103/PhysRevD.69.044026
Khoury J, Wyman M (2009) N-body simulations of DGP and degravitation theories. Phys Rev D 80:064023. doi:10.1103/PhysRevD.80.064023
Koyama K (2005) Are there ghosts in the self-accelerating brane universe? Phys Rev D 72:123511. doi:10.1103/PhysRevD.72.123511
Koyama K, Niz G, Tasinato G (2011) Analytic solutions in non-linear massive gravity. Phys Rev Lett 107:131101. doi:10.1103/PhysRevLett.107.131101
Luty MA, Porrati M, Rattazzi R (2003) Strong interactions and stability in the DGP model. JHEP 0309:029
Mizuno S, Koyama K (2010) Primordial non-Gaussianity from the DBI Galileons. Phys Rev D 82(103518). doi:10.1103/PhysRevD.82.103518
Nicolis A, Rattazzi R, Trincherini E (2009) The Galileon as a local modification of gravity. Phys Rev D 79:064036. doi:10.1103/PhysRevD.79.064036
Ondo NA, Tolley AJ (2013) Complete decoupling limit of ghost-free massive gravity
Peebles PJE, Ratra B (2003) The cosmological constant and dark energy. Rev Mod Phys 75:559–606. doi:10.1103/RevModPhys.75.559
Scherer S (2003) Introduction to chiral perturbation theory. Adv Nucl Phys 27:277
Siegel W (1986) 16/16 SUPERGRAVITY. Class Quant Grav 3:L47–L48. doi:10.1088/0264-9381/3/2/008
Silva FP, Koyama K (2009) Self-accelerating universe in galileon cosmology. Phys Rev D 80:121301. doi:10.1103/PhysRevD.80.121301
Turner MS, Widrow LM (1988) Inflation-produced, large-scale magnetic fields. Phys Rev D 37: 2743–2754. doi:10.1103/PhysRevD.37.2743. http://link.aps.org/doi/10.1103/PhysRevD.37.2743
Vainshtein AI (1972) To the problem of nonvanishing gravitation mass. Phys Lett B 39:393–394. doi:10.1016/0370-2693(72)90147-5
Weinberg S (2005) The quantum theory of fields, vol 1: Foundations. Cambridge University Press, Cambridge. ISBN 0521670535. http://www.amazon.com/Quantum-Theory-Fields-Foundations/dp/0521670535
Wyman M (2011) Galilean-invariant scalar fields can strengthen gravitational lensing. Phys Rev Lett 106:201102. doi:10.1103/PhysRevLett.106.201102
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Heisenberg, L. (2015). Introduction. In: Theoretical and Observational Consistency of Massive Gravity. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-18935-2_1
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