Advertisement

Astrophysics and Space Science

, Volume 354, Issue 2, pp 583–596 | Cite as

Antigravity in F(R) and Brans-Dicke theories

  • V. K. Oikonomou
  • N. Karagiannakis
Original Article
  • 238 Downloads

Abstract

We study antigravity in F(R)-theory originating scalar-tensor theories and also in Brans-Dicke models without cosmological constant. For the F(R) theory case, we obtain the Jordan frame antigravity scalar-tensor theory by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we shall demonstrate in detail by using some viable F(R) models, although the initial F(R) models have no antigravity, their scalar-tensor counterpart theories might or not have antigravity, a fact mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model, which we also studied numerically. In addition, regarding the Brans-Dicke model we also found some analytic cosmological solutions. Since antigravity is an unwanted feature in gravitational theories, our findings suggest that in the case of F(R) theories, antigravity does not occur in the real world described by the F(R) theory, but might occur in the Jordan frame scalar-tensor counterpart of the F(R) theory, and this happens under certain circumstances. The central goal of our study is to present all different cases in which antigravity might occur in modified gravity models.

Keywords

F(RScalar-tensor Antigravity Jordan Brans-Dicke 

References

  1. Ade, P.A.R. et al.: Phys. Rev. Lett. 112, 241101 (2014). 1403.3985v3 ADSCrossRefGoogle Scholar
  2. Amendola, L., Polarski, D., Tsujikawa, S.: Phys. Rev. Lett. 98, 131302 (2007). astro-ph/0603703v2 ADSMathSciNetCrossRefGoogle Scholar
  3. Appleby, S.A., Battye, R.A.: Phys. Lett. B 654, 7 (2007). 0705.3199v2 ADSMathSciNetCrossRefGoogle Scholar
  4. Appleby, S.A., Battye, R.A.: J. Cosmol. Astropart. Phys. 0805, 019 (2008). 0803.1081v2 ADSCrossRefGoogle Scholar
  5. Appleby, S., Battye, R., Starobinsky, A.: J. Cosmol. Astropart. Phys. 1006, 005 (2011). 0909.1737v3 ADSGoogle Scholar
  6. Arbuzova, E.V., Dolgov, A.D.: Phys. Lett. B 700, 289 (2011). 1012.1963v3 ADSCrossRefGoogle Scholar
  7. Asgari, S., Saffari, R.: Gen. Relativ. Gravit. 44, 737 (2012). 1104.5108v2 ADSCrossRefGoogle Scholar
  8. Bamba, K., Nojiri, S., Odintsov, S.D.: J. Cosmol. Astropart. Phys. 0810, 045 (2008). 0807.2575v2 ADSCrossRefGoogle Scholar
  9. Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.D.: Astrophys. Space Sci. 342, 155 (2012). 1205.3421v3 ADSCrossRefGoogle Scholar
  10. Bamba, K., Nojiri, S., Odintsov, S.D., Sáez-Gámez, D.: Phys. Lett. B 730, 136 (2014). 1401.1328v3 ADSCrossRefGoogle Scholar
  11. Bars, I., Chen, S., Steinhardt, P.J., Turok, N.: Phys. Lett. B 715, 278 (2012). 1112.2470v1 ADSCrossRefGoogle Scholar
  12. Bertolami, O., Rosenfeld, R.: Int. J. Mod. Phys. A 23, 4817 (2007). 0708.1784v2 ADSCrossRefGoogle Scholar
  13. Bertolami, O., Boehmer, C.G., Harko, T., Lobo, F.S.N.: Phys. Rev. D 75, 104016 (2007). 0704.1733v2 ADSMathSciNetCrossRefGoogle Scholar
  14. Briscese, F., Elizalde, E., Nojiri, S., Odintsov, S.D.: Phys. Lett. B 646, 105 (2007). hep-th/0612220v2 ADSCrossRefGoogle Scholar
  15. Bronnikov, K.A., Skvortsova, M.V., Starobinsky, A.A.: Gravit. Cosmol. 16, 216 (2010). 1005.3262v3 ADSMathSciNetCrossRefGoogle Scholar
  16. Capolupo, A., Capozziello, S., Vitiello, G.: Int. J. Mod. Phys. A 23, 4817 (2008). 0705.0319v1 CrossRefGoogle Scholar
  17. Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002). gr-qc/0201033v1 ADSCrossRefGoogle Scholar
  18. Capozziello, S., Laurentis, M.D.: Phys. Rep. 509, 167 (2011). 1108.6266v2 ADSMathSciNetCrossRefGoogle Scholar
  19. Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Int. J. Mod. Phys. D 12, 1969 (2003). astro-ph/0307018v1 ADSCrossRefGoogle Scholar
  20. Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005). astro-ph/0501426v1 ADSCrossRefGoogle Scholar
  21. Capozziello, S., Nojiri, S., Odintsov, S.D., Troisi, A.: Phys. Lett. B 639, 135 (2006). astro-ph/0604431v3 ADSCrossRefGoogle Scholar
  22. Caputa, P., Haque, S.S., Olson, J., Underwood, B.: Class. Quantum Gravity 30, 195013 (2013). 1306.0012v3 ADSCrossRefGoogle Scholar
  23. Carrasco, J.J.M., Chemissany, W., Kallosh, R.: Journeys Through Antigravity? (2014). 1311.3671v2
  24. Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Phys. Rev. D 70, 043528 (2004). astro-ph/0306438v2 ADSCrossRefGoogle Scholar
  25. Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: J. Cosmol. Astropart. Phys. 0502, 010 (2005). hep-th/0501096v3 ADSCrossRefGoogle Scholar
  26. Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., Zerbini, S.: Phys. Rev. D 77, 046009 (2008). 0712.4017v2 ADSCrossRefGoogle Scholar
  27. Dunsby, P.K.S., Elizalde, E., Goswami, R., Odintsov, S., Saez-Gomez, D.: Phys. Rev. D 82, 023519 (2010). 1005.2205v3 ADSCrossRefGoogle Scholar
  28. Eingorn, M., Zhuk, A.: Phys. Rev. D 84, 024023 (2011). 1104.1456v2 ADSCrossRefGoogle Scholar
  29. Eingorn, M., Novák, J., Zhuk, A.: f(R) gravity: scalar perturbations in the late universe (2014). 1401.5410v1
  30. Elizalde, E., Pozdeeva, E.O., Vernov, S.Y.: Phys. Rev. D 85, 044002 (2012). 1110.5806v3 ADSCrossRefGoogle Scholar
  31. Elizalde, E., Pozdeeva, E.O., Vernov, S.Y.: Class. Quantum Gravity 30, 035002 (2013). 1209.5957v2 ADSCrossRefGoogle Scholar
  32. Faraoni, V.: Int. J. Mod. Phys. D 11, 471 (2002). astro-ph/0110067v1 ADSCrossRefGoogle Scholar
  33. Faraoni, V.: Cosmology in Scalar-Tensor Gravity. Kluwer Academic, Dordrecht (2004) CrossRefzbMATHGoogle Scholar
  34. Faraoni, V.: Phys. Rev. D 75, 067302 (2007) ADSMathSciNetCrossRefGoogle Scholar
  35. Faulkner, T., Tegmark, M., Bunn, E.F., Mao, Y.: Phys. Rev. D 76, 063505 (2007). astro-ph/0612569v1 ADSMathSciNetCrossRefGoogle Scholar
  36. Felice, A.D., Tsujikawa, S.: Living Rev. Relativ. 13, 3 (2010). 1002.4928v2 ADSCrossRefGoogle Scholar
  37. Fujii, Y.: Prog. Theor. Phys. 99, 599 (1998). gr-qc/9708010v1 ADSCrossRefGoogle Scholar
  38. Fujii, Y., Maeda, K.-I.: The Scalar-Tensor: Theory of Gravitation. Cambridge University Press, Cambridge (2004) CrossRefzbMATHGoogle Scholar
  39. Gkigkitzis, I., Haranas, I., Ragos, O.: Phys. Int. 5(1), 103 (2014). 1406.1581v2 CrossRefGoogle Scholar
  40. Graca Morais, J.P., Bezerra, V.B.: Mod. Phys. Lett. A 27, 1250178 (2012) CrossRefGoogle Scholar
  41. Guendelman, E.I., Kaganovich, A.B.: Int. J. Mod. Phys. A 21, 4373 (2006). gr-qc/0603070v1 ADSCrossRefGoogle Scholar
  42. Haghani, Z., Harko, T., Lobo, F.S.N., Sepangi, H., Shahidi, S.: Phys. Rev. D 88, 044023 (2013). 1304.5957v3 ADSCrossRefGoogle Scholar
  43. Harko, T., Lobo, S.N., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 84, 024020 (2011). 1104.2669v2 ADSCrossRefGoogle Scholar
  44. Lee, C.-C., Geng, C.-Q., Yang, L.: Prog. Theor. Phys. 128, 415 (2012). 1201.4546v3 ADSCrossRefGoogle Scholar
  45. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003). hep-th/0307288v4 ADSCrossRefGoogle Scholar
  46. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 74, 086005 (2006). hep-th/0608008v3 ADSCrossRefGoogle Scholar
  47. Nojiri, S., Odintsov, S.D.: Int. J. Mod. Phys. A 4, 115 (2007). hep-th/0601213v5 Google Scholar
  48. Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011). 1011.0544v4 ADSMathSciNetCrossRefGoogle Scholar
  49. Odintsov, S.D., Sáez-Gómez, D.: Phys. Lett. B 725, 4373 (2013). 1304.5411v3 CrossRefGoogle Scholar
  50. Oikonomou, V.K., Karagiannakis, N.: Study of antigravity in an F(R) model and in Brans-Dicke theory with cosmological constant (2014). 1408.0398v1
  51. Oltean, M., Brandenberger, R.: Cosmological perturbations in antigravity (2014). 1406.7318v1
  52. Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003). astro-ph/0207347v2 ADSCrossRefGoogle Scholar
  53. Sharif, M., Arif, S.: Mod. Phys. Lett. A 27, 1250138 (2012). 1302.1191v1 ADSCrossRefGoogle Scholar
  54. Sharif, M., Zubair, M.: J. Cosmol. Astropart. Phys. 1311, 042 (2013) ADSCrossRefGoogle Scholar
  55. Sharif, M., Zubair, M.: Astrophys. Space Sci. 349, 457 (2014) ADSCrossRefGoogle Scholar
  56. Song, Y.-S., Hu, W., Sawicki, I.: Phys. Rev. D 75, 044004 (2007). astro-ph/0610532v2 ADSCrossRefGoogle Scholar
  57. Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010). 0805.1726v4 ADSCrossRefGoogle Scholar
  58. Srivastava, S.K.: Int. J. Mod. Phys. A 22, 1123 (2007) ADSCrossRefGoogle Scholar
  59. Starobinsky, A.A.: JETP Lett. 86, 157 (2007). 0706.2041v2 ADSCrossRefGoogle Scholar
  60. Tsujikawa, S.: Phys. Rev. D 77, 023507 (2008). 0709.1391v2 ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Department of Theoretical PhysicsAristotle University of ThessalonikiThessalonikiGreece
  3. 3.Polytechnic SchoolAristotle University of ThessalonikiThessalonikiGreece

Personalised recommendations