Special Issue on New trends in Theory of GravityNo Access

Problems of massive gravities

S. Deser

Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, CA 91125, USA

Physics Department, Brandeis University, Waltham, MA 02454, USA

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K. Izumi

Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan

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Y. C. Ong

Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden

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, and

A. Waldron

Department of Mathematics, University of California, Davis, CA 95616, USA

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https://doi.org/10.1142/S0217732315400064Cited by:35 (Source: Crossref)

Abstract

The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring explicit solutions. We review this method and its application to massive gravity (mGR) theories to show the limitations of these models' physical viability: Among their problems are loss of unique evolution, superluminal signals, matter coupling inconsistencies and micro-acausality (propagation of signals around local closed time-like curves (CTCs)/closed causal curves (CCCs)). We extend previous no-go results to the entire three-parameter range of mGR theories. It is also argued that bimetric models suffer a similar fate.

Keywords:

References

1. A. Salam and J. Strathdee, Phys. Rev. 184, 1750, 1760 (1969); C. J. Isham, A. Salam and J. Strathdee, Phys. Lett. B 31, 300 (1970). Google Scholar
2. B. Zumino, Effective Lagrangians and broken symmetries, in Lectures on Elementary Particles and Quantum Field Theory, Vol. 2, eds. S. Deser, M. Grisaru and H. Pendleton (MIT Press, 1970), p. 437. Google Scholar
3. D. Boulware and S. Deser, Phys. Rev. D 6, 3368 (1972); Phys. Lett. B 40, 227 (1972). Google Scholar
4. M. Fierz and W. Pauli, Proc. Roy. Soc. Lond. A 173, 211 (1939); M. Fierz, Helv. Phys. Acta 12, 3 (1939). Google Scholar
5. C. de Rham and G. Gabadadze, Phys. Rev. D 82, 044020 (2010); C. de Rham, G. Gabadadze and A. J. Tolley, Phys. Rev. Lett. 106, 231101 (2011); Phys. Lett. B 711, 190 (2012); JHEP 1111, 093 (2011). Google Scholar
6. K. Hinterbichler, Rev. Mod. Phys. 84, 671 (2012). Crossref, Web of Science, ADS, Google Scholar
7. C. de Rham, Living Rev. Relativ. 17, 7 (2014). Crossref, Web of Science, ADS, Google Scholar
8. S. F. Hassan and R. A. Rosen, Phys. Rev. Lett. 108, 041101 (2012); S. F. Hassan, R. A. Rosen and A. Schmidt-May, JHEP 02, 026 (2012); S. F. Hassan and R. A. Rosen, ibid. 04, 123 (2012); S. Hassan, A. Schmidt-May and M. von Strauss, Phys. Lett. B 715, 335 (2012). Google Scholar
9. J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, 1965). Google Scholar
10. K. Johnson and E. C. G. Sudarshan, Ann. Phys. 13, 126 (1961). Crossref, Web of Science, ADS, Google Scholar
11. G. Velo and D. Zwanziger, Phys. Rev. 186, 1337 (1969); ibid. 188, 2218 (1969). Google Scholar
12. C. Deffayet, J. Mourad and G. Zahariade, J. Cosmol. Astropart. Phys. 1301, 031 (2013). Google Scholar
13. S. Deser and A. Waldron, Phys. Rev. Lett. 110, 111101 (2013). Crossref, Web of Science, ADS, Google Scholar
14. S. Deser, M. Sandora and A. Waldron, Phys. Rev. D 87, 101501 (2013). Crossref, Web of Science, ADS, Google Scholar
15. S. Deser, M. Sandora, A. Waldron and G. Zahariade, Phys. Rev. D 90, 104043 (2014). Crossref, Web of Science, ADS, Google Scholar
16. C. Burrage, C. de Rham, L. Heisenberg and A. J. Tolley, J. Cosmol. Astropart. Phys. 1207, 004 (2012); P. de Fromont, C. de Rham, L. Heisenberg and A. Matas, JHEP 1307, 067 (2013); A. Gruzinov, arXiv:1106.3972. Google Scholar
17. K. Izumi and Y. C. Ong, Class. Quantum Grav. 30, 184008 (2013). Crossref, Web of Science, ADS, Google Scholar
18. S. Deser, K. Izumi, Y. C. Ong and A. Waldron, Phys. Lett. B 726, 544 (2013); arXiv:1312.1115. Google Scholar
19. S. Deser, M. Sandora and A. Waldron, Phys. Rev. D 88, 081501 (2013). Crossref, Web of Science, ADS, Google Scholar
20. R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2 (Wiley-Interscience, 1962), pp. 590, 596. Google Scholar
21. H. Chen, J. M. Nester and H.-J. Yo, Phys. Pol. B 29, 961 (1998). Web of Science, Google Scholar
22. Y. C. Ong, K. Izumi, J. M. Nester and P. Chen, Phys. Rev. D 88, 024019 (2013). Crossref, Web of Science, ADS, Google Scholar
23. K. Izumi, J.-A. Gu and Y. C. Ong, Phys. Rev. D 89, 084025 (2014). Crossref, Web of Science, ADS, Google Scholar
24. K. Izumi, Phys. Rev. D 90, 044037 (2014); H. Reall, N. Tanahashi and B. Way, Class. Quantum Grav. 31, 205005 (2014); arXiv:1409.3874. Google Scholar
25. R. L. Arnowitt, S. Deser and C. W. Misner, Phys. Rev. 116, 1322 (1959); ibid. 117, 1595 (1960). Google Scholar
26. H. Georgi, Weak Interactions and Modern Particle Theory (Dover Publications, 2009); N. Arkani-Hamed, H. Georgi and M. D. Schwartz, Ann. Phys. 305, 96 (2003). Google Scholar
27. N. Kaloper, A. Padilla, P. Saffin and D. Stefanyszyn, arXiv:1409.3243. Google Scholar
28. C. Deffayet, J. Mourad and G. Zahariade, JHEP 1303, 086 (2013). Crossref, Web of Science, ADS, Google Scholar
29. A. H. Chamseddine and V. Mukhanov, JHEP 1108, 091 (2011). Crossref, Web of Science, ADS, Google Scholar
30. A. H. Chamseddine and M. S. Volkov, Phys. Lett. B 704, 652 (2011). Crossref, Web of Science, ADS, Google Scholar
31. K. Hinterbichler and R. A. Rosen, JHEP 1207, 047 (2012). Crossref, Web of Science, ADS, Google Scholar
32. S. F. Hassan, A. Schmidt-May and M. von Strauss, arXiv:1204.5202. Google Scholar
33. K. Nomura and J. Soda, Phys. Rev. D 86, 084052 (2012). Crossref, Web of Science, ADS, Google Scholar
34. R. Geroch, arXiv:1005.1614. Google Scholar
35. H. Andréka, J. X. Madarász, I. Németi, M. Stannett and G. Székely, Class. Quantum Grav. 31, 095005 (2014). Crossref, Web of Science, Google Scholar
36. S. Deser, R. Jackiw and G. ’t Hooft, Phys. Rev. Lett. 68, 267 (1992). Crossref, Web of Science, ADS, Google Scholar
37. S. Deser and A. Waldron, Phys. Rev. D 89, 027503 (2014). Crossref, Web of Science, ADS, Google Scholar
38. İ. Güllü and B. Tekin, Phys. Lett. B 728, 268 (2014). Crossref, Web of Science, ADS, Google Scholar
39. Y. Yamashita, A. De Felice and T. Tanaka, arXiv:1408.0487. Google Scholar
40. C. de Rham, L. Heisenberg and R. H. Ribeiro, arXiv:1408.1678. Google Scholar
41. J. Noller and S. Melville, J. Cosmol. Astropart. Phys. 01, 003 (2015); V. O. Soloviev, arXiv:1410.0048. Google Scholar
42. S. Deser and R. I. Nepomechie, Ann. Phys. 154, 396 (1984); Phys. Lett. B 132, 321 (1983). Google Scholar
43. S. Deser and A. Waldron, Phys. Rev. Lett. 87, 031601 (2001); Nucl. Phys. B 607, 577 (2001); Phys. Lett. B 508, 347 (2001); ibid. 513, 137 (2001); Nucl. Phys. B 662, 379 (2003); Phys. Lett. B 603, 30 (2004); Phys. Rev. D 74, 084036 (2006); M. Grigoriev and A. Waldron, Nucl. Phys. B 853, 291 (2011); Phys. Rev. D 87, 087702 (2013); S. Deser, E. Joung and A. Waldron, ibid. 86, 104004 (2012); J. Phys. A 46, 214019 (2013). Google Scholar
44. C. de Rham and S. Renaux-Petel, J. Cosmol. Astropart. Phys. 1301, 035 (2013). Crossref, Web of Science, ADS, Google Scholar
45. S. F. Hassan, A. Schmidt-May and M. von Strauss, arXiv:1208.1797; Y. Akrami, T. S. Koivisto, D. F. Mota and M. Sandstad, J. Cosmol. Astropart. Phys. 1310, 046 (2013). Google Scholar
46. C. de Rham, K. Hinterbichler, R. A. Rosen and A. J. Tolley, Phys. Rev. D 88, 024003 (2013). Crossref, Web of Science, ADS, Google Scholar
47. E. Joung, W. Li and M. Taronna, Nucl. Phys. B 886, 712 (2014) ; Y. M. Zinoviev, arXiv:1405.4065. Google Scholar
48. S. Deser, K. Izumi, Y. C. Ong, A. Waldron and G. Zahariade, in preparation. Google Scholar