Advertisement

General Relativity and Gravitation

, Volume 38, Issue 7, pp 1215–1232 | Cite as

Brane World Corrections to Newton’s Law

  • K. A. Bronnikov
  • S. A. Kononogov
  • V. N. Melnikov
Review

Abstract

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After giving a brief general exposition, we review in more detail the predicted corrections to Newton’s law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein–Gauss–Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton’s law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.

Keywords

Brane world Multidimensional gravity Newton’s law Gravitational constant variation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Melnikov, V.N.: Multidimensional Classical and Quantum Cosmology and Gravitation. Exact Solutions and Variations of Constants, CBPF-NF-051/93, Rio de Janeiro, (1993)Google Scholar
  2. 2.
    Melnikov, V.N.: In: Novello, M.(ed.) Cosmology and Gravitation, p. 147. Editions Frontieres, Singapore, (1994)Google Scholar
  3. 3.
    Melnikov, V.N.: Multidimensional Cosmology and Gravitation, CBPF-MO-002/95, Rio de Janeiro, (1995)Google Scholar
  4. 4.
    Melnikov, V.N.: In: Novello, M. (ed.) Cosmology and Gravitation. II, p. 465. Editions Frontieres, Singapore, (1996)Google Scholar
  5. 5.
    Melnikov, V.N.: Exact Solutions in Multidimensional Gravity and Cosmology III, pp. 297. CBPF-MO-03/02, Rio de Janeiro, (2002)Google Scholar
  6. 6.
    Staniukovich, K.P., Melnikov, V.N.: Hydrodynamics, Fields and Constants in the Theory of Gravitation, Energoatomizdat, Moscow, (1983) (in Russian)Google Scholar
  7. 7.
    Melnikov, V.N.: Fields and Constants in the Theory of Gravitation, 134 pp. CBPF-MO-02/02, Rio de Janeiro, (2002)Google Scholar
  8. 8.
    Melnikov, V.N.: In: de Sabbata, V., Melnikov, V.N (eds.) Gravitational Measurements Fundamental Metrology and Constants, p. 283. Kluwer, Dordrecht, (1988)Google Scholar
  9. 9.
    De Sabbata V., Melnikov V.N., Pronin P.I. (1992). Theoretical approach to Treatment of nonnewtonian interactions. Prog. Theor. Phys. 88:623CrossRefADSGoogle Scholar
  10. 10.
    Melnikov V.N. (1994). Int. J. Theor. Phys. 33 (7):1569–1579CrossRefGoogle Scholar
  11. 11.
    Melnikov, V.N.: Proceedings. NASA/JPL Workshop on Fundamental Physics in Microgravity, NASA, pp. 4.1- 4.17. Document D-21522, (2001)Google Scholar
  12. 12.
    Kononogov, S.A., Melnikov, V.N.: Izm. Tekhnika [Measurement Techniques] 6, 1 (2005)Google Scholar
  13. 13.
    Achilli V. et al. (1997). Nuovo Cim. B 12:775Google Scholar
  14. 14.
    Anderson J.D. et al. (1995). Phys. Rev. Lett. 75:3602CrossRefADSGoogle Scholar
  15. 15.
    Anderson J.D. et al. (1998). Phys. Rev. Lett. 81:2858CrossRefADSGoogle Scholar
  16. 16.
    Ranada A. (2002). Europhys. Lett. 63:653CrossRefADSGoogle Scholar
  17. 17.
    Das A. et al. (2003). J. Math. Phys. 44:5536CrossRefGoogle Scholar
  18. 18.
    Modanese G. (1999). Nucl. Phys. 556:397; gr-qc/9903085MATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Mansouri R., Nasseri, F., Khorrami, M.: A 259 194 (1999) gr-qc/9905052Google Scholar
  20. 20.
    Oestvang D. (2002). Class. Quantum Grav. 19:4131 gr-qc/9910054MATHCrossRefADSGoogle Scholar
  21. 21.
    Belayev, W.B.: gr-qc/9903016Google Scholar
  22. 22.
    Moffat, J.W.: Modified gravitational theory and the pioneer 10 and 11 spacecraft anomalous acceleration, gr-qc/0405076Google Scholar
  23. 23.
    Milgrom M. (2001). Acta. Phys. Pol. B 32:3613ADSGoogle Scholar
  24. 24.
    Bekenstein J. (2004). Phys. Rev. D 70:083509; astro-ph/0403694CrossRefADSGoogle Scholar
  25. 25.
    Calchi Novati S. et al. (2000). Grav & Cosmol 6:173; astro-ph/0005104MATHADSMathSciNetGoogle Scholar
  26. 26.
    Mbelek, J.-P., Lachieze-Rey, M.: Long-range acceleration induced by a scalar field external to gravity and the indication from Pioneer 10/11, Galileo and Ulysses data, gr-qc/9910105Google Scholar
  27. 27.
    Jaekel H.T., Reynaud S. (2005). Class. Quantum Grav. 22:2135MATHCrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Jaekel H.T., Reynaud S. (2005). Mod. Phys. Lett. A 20:1047CrossRefADSGoogle Scholar
  29. 29.
    Turyshev, S., Nieto, M., Anderson, J.: Invited talk, The XXII Texas Symposium on Relativistic Astrophysics, Stanford University, December 13–17, 2004; gr-qc/0503021Google Scholar
  30. 30.
    Sherk, J.: 88, Phys. Lett. B 265, (1979).Google Scholar
  31. 31.
    Moody J.E., Wilczek F. (1984). Phys. Rev. D 30:130CrossRefADSGoogle Scholar
  32. 32.
    Fayer, P.: Phys. Lett. B 277, 127 (1989)Google Scholar
  33. 33.
    Weinberg S. (1989). Rev. Mod. Phys. 61:1MATHCrossRefADSMathSciNetGoogle Scholar
  34. 34.
    Long J.S. et al. (2003). Nature 421:922CrossRefADSGoogle Scholar
  35. 35.
    Akama M. (1987). Prog. Theor. Phys. 78:184CrossRefADSGoogle Scholar
  36. 36.
    Rubakov V.A., Shaposhnikov M.E. (1983). Phys. Lett. B 152:136ADSGoogle Scholar
  37. 37.
    Horava P., Witten E. (1996). Nucl. Phys. 460:506CrossRefADSMathSciNetGoogle Scholar
  38. 38.
    Horava P., Witten E. (1996). Nucl. Phys. 475:94MATHCrossRefADSMathSciNetGoogle Scholar
  39. 39.
    Randall L., Sundrum R. (1999). Phys. Rev. Lett. 83:3370; hep-ph/9905221MATHCrossRefADSMathSciNetGoogle Scholar
  40. 40.
    Rubakov V.A. (2001). Large and infinite extra dimensions. Phys. Usp. 44:871; hep-ph/0104152CrossRefGoogle Scholar
  41. 41.
    Maartens, R.: Geometry and dynamics of the brane world, gr-qc/0101059Google Scholar
  42. 42.
    Langlois, D.: Gravitation and cosmology in a brane universe, gr-qc/0207047Google Scholar
  43. 43.
    Nojiri, S., Odintsov, S.D., Ogushi, S.: Int. J. Mod. Phys. A 17, 4809 (2002); hep-th/0205187Google Scholar
  44. 44.
    Brax, Ph., van de Bruck, V.: Cosmology and brane worlds: a review, hep-th/0303095.Google Scholar
  45. 45.
    Maartens R. (2004). Brane world gravity. Living Rev. Relativity 7: 7ADSGoogle Scholar
  46. 46.
    Coley, A.A.: The Dynamics of Brane-World Cosmological Models, astro-ph/0504226Google Scholar
  47. 47.
    Milgrom M. Astroph 270 365, 371, 384 (1983)Google Scholar
  48. 48.
    Mouslopoulos, S.: Multi-scale physics from multi-braneworlds, hep-th/0503065Google Scholar
  49. 49.
    Deruelle, N.: Linearized gravity on branes from Newton’s law to cosmological perturbations, gr-qc/0301036Google Scholar
  50. 50.
    Deruelle N., Sasaki M. (2003). Newton’s law on an ‘Einstein-Gauss-Bonnet’ brane. Prog. Theor. Phys. 110:441; gr-qc/0306032MATHCrossRefADSGoogle Scholar
  51. 51.
    Azam M., Sami M. (2005). Many-body treatment of white dwarfs and neutron stars on the brane. Phys. Rev. D 72:024024; gr-qc/0502026CrossRefADSGoogle Scholar
  52. 52.
    Rubakov, V.A.: Strong coupling in brane-induced gravity in 5 dimensions, hep-th/0303125Google Scholar
  53. 53.
    Parry, M., Pichler, S., Deeg, D.: Higher-derivative gravity in brane world models, JCAP 0504, 014 (2005); hep-ph/0502048Google Scholar
  54. 54.
    Sher, M., Sullivan, K.A.: Experimentally probing the shape of extra dimensions, hep-ph/0503262Google Scholar
  55. 55.
    Callin, P., Ravndall, F.: Higher-order corrections to the Newtonian integration potential in the Randall-Sundrum model, Phys. Rev. D 70 104009 (2004); hep-ph/0403302Google Scholar
  56. 56.
    Shaposhnikov, M., Tinyakov, P., Zuleta, K.: Quasilocalized gravity without asymptotic flatness, Phys. Rev. D 70 104019 (2004); hep-th/0411031Google Scholar
  57. 57.
    Randall L., Sundrum R. (1999). Phys. Rev. Lett. 83:4690; hep-ph/9906064MATHCrossRefADSMathSciNetGoogle Scholar
  58. 58.
    Kiritsis E., Tetradis T., Tomaras T.N. (2002). J. High Energy Phys. 03: 019; hep-th/0202037CrossRefADSMathSciNetGoogle Scholar
  59. 59.
    Ghoroku K., Nakamura A., Yahiro M. (2003). Phys. Lett. B 571:223; hep-th/0303068MATHCrossRefADSMathSciNetGoogle Scholar
  60. 60.
    Garriga J., Tanaka T. (2000). Phys. Rev. Lett. 84:2778; hep-th/9911055MATHCrossRefADSMathSciNetGoogle Scholar
  61. 61.
    Giddings S.B., Katz E., Randall L. (2000). J. High Energy Phys. 03:023; hep-th/0002091CrossRefADSMathSciNetGoogle Scholar
  62. 62.
    Chung, D.J.H., Everett, L., Davoudiasl, H.: Phys. Rev. D 64, 065002 (2001); hep-ph/0010103Google Scholar
  63. 63.
    Deruelle, N., Doležel, T.: Phys. Rev. D 64, 103506 (2001); gr-qc/0105118Google Scholar
  64. 64.
    Jung E., Kim S., Park D.K. (2003). Newton law on the generalized singular brane with and without 4d induced gravity. Nucl. Phys. 669:306; hep-th/0305156MATHCrossRefADSMathSciNetGoogle Scholar
  65. 65.
    Dvali G., Gabadadze G., Porrati M. (2000). Phys. Lett. B 485:208; hep-th/0005016MATHCrossRefADSMathSciNetGoogle Scholar
  66. 66.
    Sahni, V., Shtanov, Y., Viznyuk, A.: Cosmic mimicry: Is LCDM a braneworld in disguise?, JCAP 0512, 005 (2005); astro-ph/0505004Google Scholar
  67. 67.
    Hull C. (1998). JHEP 9807:021CrossRefADSMathSciNetGoogle Scholar
  68. 68.
    Strominger A. (2001). JHEP 0110:034; hep-th/0106113CrossRefADSMathSciNetGoogle Scholar
  69. 69.
    Nojiri S., Odintsov S.D. (2002). Newton potential in de Sitter braneworld. Phys. Lett. B 548:215–223; hep-th/0209066MATHCrossRefADSMathSciNetGoogle Scholar
  70. 70.
    Kehagias A., Tamvakis K. (2002). Graviton localization and Newton law for a dS4 brane in 5D bulk. Class. Quantum Grav. 19:L185; hep-th/0205009MATHCrossRefADSMathSciNetGoogle Scholar
  71. 71.
    Bronnikov K.A., Meierovich B.E. (2003). A general thick brane supported by a scalar field. Grav. Cosmol. 9:313; gr-qc/0402030MATHADSMathSciNetGoogle Scholar
  72. 72.
    Abdyrakhmanov S.T., Bronnikov K.A., Meierovich B.E. (2005). Uniqueness of RS2 type thick branes supported by a scalar field. Grav. Cosmol. 11:82; gr-qc/0503055MATHADSGoogle Scholar
  73. 73.
    Nojiri S., Obregon O., Odintsov O.D., Ogushi S. (2000). Phys. Rev. D 62:064017; hep-th/0003148CrossRefADSMathSciNetGoogle Scholar
  74. 74.
    Bozza V., Gasperini G., Veneziano G. (2001). Scalar fluctuations in dilatonic brane worlds. Nucl. Phys. 619:191; hep-th/0111268MATHCrossRefADSMathSciNetGoogle Scholar
  75. 75.
    Gregory R., Rubakov V.A., Sibiryakov S.M. (2000). Opening up extra dimensions at ultra-high scales. Phys. Rev. Lett. 84:5928; hep-th/0002072CrossRefADSMathSciNetGoogle Scholar
  76. 76.
    Gregory, R., Rubakov, V.A., Sibiryakov, S.M.: Gravity and anti-gravity in a brane world with metastable gravitons, B 489, 203 (2000); hep-th/0003045Google Scholar
  77. 77.
    Smolyakov, M.N., Volobuev, I.P.: Linearized gravity, Newtonian limit and light deflection in RS1 model, hep-th/0208025Google Scholar
  78. 78.
    Arnowitt, R., Dent, J.: Gravitational forces on the branes, hep-th/0409308Google Scholar
  79. 79.
    Shtanov Y., Viznyuk A. (2005). Class. Quantum Grav. 22:987; hep-th/0312261MATHCrossRefADSMathSciNetGoogle Scholar
  80. 80.
    Smolyakov M.N. (2004). Brane induced gravity in warped backgrounds and the absence of the radion. Nucl. Phys. 695:301–312; hep-th/0403034MATHCrossRefADSMathSciNetGoogle Scholar
  81. 81.
    Smolyakov M.N. (2005). On the long-range gravity in warped backgrounds. Nucl. Phys. 724:397–405; hep-th/0502116MATHCrossRefADSMathSciNetGoogle Scholar
  82. 82.
    Kogan I.I., Mouslopoulos S., Papazoglou A., Ross G.G. (2001). Multi-Localization in Multi-Brane Worlds. Nucl. Phys. 615:191–218; hep-ph/0107307MATHCrossRefADSMathSciNetGoogle Scholar
  83. 83.
    Kogan, I.I., Mouslopoulos, S., Papazoglou, A., Ross, G.G.: Multigravity in six dimensions: Generating bounces with flat positive tension branes, Phys. Rev. D 64 124014 (2001), hep-th/0107086Google Scholar
  84. 84.
    Kogan I.I., Mouslopoulos S., Papazoglou A., Pilo L. (2002). Radion in multibrane world. Nucl. Phys. 625:179; hep-th/0105255MATHCrossRefADSGoogle Scholar
  85. 85.
    Kogan I.I., Mouslopoulos S., Papazoglou A., Ross G.G. (2001). Multi-brane worlds and modification of gravity at large scales. Nucl. Phys. 595:225; hep-th/0006030MATHCrossRefADSMathSciNetGoogle Scholar
  86. 86.
    Roessl, E., Topological defects and gravity in theories with extra dimensions, hep-th/0508099Google Scholar
  87. 87.
    Gherghetta R., Roessl E., Shaposhnikov M. (2000). Phys. Lett. B 491:353MATHCrossRefADSMathSciNetGoogle Scholar
  88. 88.
    Roessl E., Shaposhnikov, M.: Phys. Rev. D 66 084008 (2002)Google Scholar
  89. 89.
    Cohen A.G., Kaplan D.B. (1999). Phys. Lett. B 470:52MATHCrossRefADSMathSciNetGoogle Scholar
  90. 90.
    Gregory R. (2000). Phys. Rev. Lett. 84:2564MATHCrossRefADSMathSciNetGoogle Scholar
  91. 91.
    Olasagasti, I., Vilenkin, A.: Phys. Rev. D 62 044014 (2000)Google Scholar
  92. 92.
    Gherghetta T., Shaposhnikov M. (2000). Phys. Rev. Lett. 85:240CrossRefADSMathSciNetGoogle Scholar
  93. 93.
    Bronnikov K.A., Meierovich B.E. (2005). Gravitating global monopoles in extra dimensions and the brane world concept. Sov. phys. JETP 101:1036–1052; gr-qc/0507032CrossRefADSGoogle Scholar
  94. 94.
    Kirillov A.A. (2006). The nature of dark matter. Phys. Lett. B 632:453–462; astro-ph/0505131CrossRefADSMathSciNetGoogle Scholar
  95. 95.
    Kirillov, A.A.: Modification of the field theory and the dark matter problem, astro-ph/0405623Google Scholar
  96. 96.
    Pal, S.: An alternative to dark matter: do braneworld effects hold the key? astro-ph/0512494Google Scholar
  97. 97.
    Shiromizu, T., Maeda, K., Sasaki, M., Phys. Rev. D 62 024012 (2000)Google Scholar
  98. 98.
    Gogberashvili M., Midodashvili P. (2001). Phys. Lett. B 515:447MATHCrossRefADSMathSciNetGoogle Scholar
  99. 99.
    Gogberashvili M., Midodashvili P. (2003). Europhys. Lett. 61:308CrossRefADSMathSciNetGoogle Scholar
  100. 100.
    Gogberashvili M., Singleton D. Phys. Rev. D 69 026004 (2004).Google Scholar
  101. 101.
    Oda I. (2003). Phys. Lett. B 571:235MATHCrossRefADSMathSciNetGoogle Scholar
  102. 102.
    Gogberashvili M., Singleton D. (2004). Phys. Lett. B 582:95CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • K. A. Bronnikov
    • 1
    • 2
  • S. A. Kononogov
    • 1
  • V. N. Melnikov
    • 1
    • 2
  1. 1.Center for Gravitation and Fundamental MetrologyVNIIMSMoscowRussia
  2. 2.Institute of Gravitation and CosmologyPeoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations