Abstract
We consider a general approach to describing the interaction in multigravity models in a D-dimensional space-time. We present various possibilities for generalizing the invariant volume. We derive the most general form of the interaction potential, which becomes a Pauli-Fierz-type model in the bigravity case. Analyzing this model in detail in the (3+1)-expansion formalism and also requiring the absence of ghosts leads to this bigravity model being completely equivalent to the Pauli-Fierz model. We thus in a concrete example show that introducing an interaction between metrics is equivalent to introducing the graviton mass.
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References
P. D. Mannheim, Progr. Part. Nucl. Phys., 56, 340–445 (2006).
H. F. M. Goenner, Living Rev. Relativ., 7, 2004–2 (2004).
S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley, New York (1972).
R. M. Wald, General Relativity, Univ. Chicago Press, Chicago (1984).
C. J. Isham, A. Salam, and J. Strathdee, Phys. Rev. D, 3, 867–873 (1971).
P. C. Aichelburg, R. Mansouri, and H. K. Urbantke, Phys. Rev. Lett., 27, 1533–1534 (1971).
P. C. Aichelburg, Phys. Rev. D, 8, 377–384 (1973).
I. I. Kogan and G. G. Ross, Phys. Lett. B, 485, 255–262 (2000).
I. I. Kogan, S. Mouslopoulos, A. Papazoglou, and G. G. Ross, Nucl. Phys. B, 595, 225–249 (2001).
I. I. Kogan, S. Mouslopoulos, and A. Papazoglou, Phys. Lett. B, 501, 140–149 (2001).
C. Deffayet and J. Mourad, Phys. Lett. B, 589, 48–58 (2004).
C. Deffayet and J. Mourad, Internat. J. Theoret. Phys., 43, 855–864 (2004).
R. Garattini, J. Phys. A, 40, 7055–7060 (2007).
D. Blas, AIP Conf. Proc., 841, 397–401 (2006).
S. Hannestad, Internat. J. Mod. Phys. A, 21, 1938–1949 (2006); arXiv:astro-ph/0509320v2 (2005).
A. A. Grib and Yu. V. Pavlov, Grav. Cosmol., 12, 159–162 (2006).
S. L. Dubovsky, P. G. Tinyakov, and I. I. Tkachev, Phys. Rev. Lett., 94, 181102 (2005).
T. Damour, I. I. Kogan, and A. Papazoglou, Phys. Rev. D, 66, 104025 (2002).
C. Deffayet, G. Dvali, and G. Gabadadze, Phys. Rev. D, 65, 044023 (2002).
T. Damour and I. I. Kogan, Phys. Rev. D, 66, 104024 (2002).
C. de Rham and G. Gabadadze, Phys. Rev. D, 82, 044020 (2010).
D. G. Boulware and S. Deser, Phys. Rev. D, 6, 3368–3382 (1972).
K. Koyama, G. Niz, and G. Tasinato, Phys. Rev D, 84, 064033 (2011).
C. de Rham, G. Gabadadze, and A. J. Tolley, JHEP, 1111, 093 (2011).
A. H. Chamseddine and V. Mukhanov, JHEP, 1108, 091 (2011).
S. F. Hassan and R. A. Rosen, Phys. Rev. Lett., 108, 041101 (2012).
V. I. Zakharov, JETP Lett., 12, 312–315 (1970).
H. van Dam and M. J. G. Veltman, Nucl. Phys. B, 22, 397–411 (1970).
A. I. Vainshtein, Phys. Lett. B, 39, 393–394 (1972).
E. Babichev, C. Deffayet, and R. Ziour, Phys. Rev. D, 82, 104008 (2010).
V. A. Rubakov and P. G. Tinyakov, Phys.-Usp., 51, 759–792 (2008).
K. Hinterbichler, Rev. Modern Phys., 84, 671–710 (2012).
N. Boulanger, T. Damour, L. Gualtieri, and M. Henneaux, Nucl. Phys. B, 597, 127–171 (2001).
S. A. Duplij and A. T. Kotvytskiy, J. Kharkiv Univ. Ser. Nuclei, Particles, Fields, 784, No. 4(36), 61–66 (2007).
R. Hermann, Quantum and Fermion Differential Geometry Part A, Mathematical Science Press, Brookline, Mass. (1977).
A. T. Kotvytskiy and D. V. Kruchkov, Acta Polytechnika, 51, 54–58 (2011).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 177, No. 1, pp. 137–150, October, 2013.
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Duplij, S.A., Kotvytskiy, A.T. Generalized interaction in multigravity. Theor Math Phys 177, 1400–1411 (2013). https://doi.org/10.1007/s11232-013-0112-3
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DOI: https://doi.org/10.1007/s11232-013-0112-3