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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Time axis has been properly rescaled so that t=1 in the graph corresponds to t=10−46 s. The same applies to all figures that follow.
The same set of initial conditions and time axis rescaling is applied to all plots of this article.
References
Ade, P.A.R. et al.: Phys. Rev. Lett. 112, 241101 (2014). 1403.3985v3
Amendola, L., Polarski, D., Tsujikawa, S.: Phys. Rev. Lett. 98, 131302 (2007). astro-ph/0603703v2
Appleby, S.A., Battye, R.A.: Phys. Lett. B 654, 7 (2007). 0705.3199v2
Appleby, S.A., Battye, R.A.: J. Cosmol. Astropart. Phys. 0805, 019 (2008). 0803.1081v2
Appleby, S., Battye, R., Starobinsky, A.: J. Cosmol. Astropart. Phys. 1006, 005 (2011). 0909.1737v3
Arbuzova, E.V., Dolgov, A.D.: Phys. Lett. B 700, 289 (2011). 1012.1963v3
Asgari, S., Saffari, R.: Gen. Relativ. Gravit. 44, 737 (2012). 1104.5108v2
Bamba, K., Nojiri, S., Odintsov, S.D.: J. Cosmol. Astropart. Phys. 0810, 045 (2008). 0807.2575v2
Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.D.: Astrophys. Space Sci. 342, 155 (2012). 1205.3421v3
Bamba, K., Nojiri, S., Odintsov, S.D., Sáez-Gámez, D.: Phys. Lett. B 730, 136 (2014). 1401.1328v3
Bars, I., Chen, S., Steinhardt, P.J., Turok, N.: Phys. Lett. B 715, 278 (2012). 1112.2470v1
Bertolami, O., Rosenfeld, R.: Int. J. Mod. Phys. A 23, 4817 (2007). 0708.1784v2
Bertolami, O., Boehmer, C.G., Harko, T., Lobo, F.S.N.: Phys. Rev. D 75, 104016 (2007). 0704.1733v2
Briscese, F., Elizalde, E., Nojiri, S., Odintsov, S.D.: Phys. Lett. B 646, 105 (2007). hep-th/0612220v2
Bronnikov, K.A., Skvortsova, M.V., Starobinsky, A.A.: Gravit. Cosmol. 16, 216 (2010). 1005.3262v3
Capolupo, A., Capozziello, S., Vitiello, G.: Int. J. Mod. Phys. A 23, 4817 (2008). 0705.0319v1
Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002). gr-qc/0201033v1
Capozziello, S., Laurentis, M.D.: Phys. Rep. 509, 167 (2011). 1108.6266v2
Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Int. J. Mod. Phys. D 12, 1969 (2003). astro-ph/0307018v1
Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005). astro-ph/0501426v1
Capozziello, S., Nojiri, S., Odintsov, S.D., Troisi, A.: Phys. Lett. B 639, 135 (2006). astro-ph/0604431v3
Caputa, P., Haque, S.S., Olson, J., Underwood, B.: Class. Quantum Gravity 30, 195013 (2013). 1306.0012v3
Carrasco, J.J.M., Chemissany, W., Kallosh, R.: Journeys Through Antigravity? (2014). 1311.3671v2
Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Phys. Rev. D 70, 043528 (2004). astro-ph/0306438v2
Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: J. Cosmol. Astropart. Phys. 0502, 010 (2005). hep-th/0501096v3
Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., Zerbini, S.: Phys. Rev. D 77, 046009 (2008). 0712.4017v2
Dunsby, P.K.S., Elizalde, E., Goswami, R., Odintsov, S., Saez-Gomez, D.: Phys. Rev. D 82, 023519 (2010). 1005.2205v3
Eingorn, M., Zhuk, A.: Phys. Rev. D 84, 024023 (2011). 1104.1456v2
Eingorn, M., Novák, J., Zhuk, A.: f(R) gravity: scalar perturbations in the late universe (2014). 1401.5410v1
Elizalde, E., Pozdeeva, E.O., Vernov, S.Y.: Phys. Rev. D 85, 044002 (2012). 1110.5806v3
Elizalde, E., Pozdeeva, E.O., Vernov, S.Y.: Class. Quantum Gravity 30, 035002 (2013). 1209.5957v2
Faraoni, V.: Int. J. Mod. Phys. D 11, 471 (2002). astro-ph/0110067v1
Faraoni, V.: Cosmology in Scalar-Tensor Gravity. Kluwer Academic, Dordrecht (2004)
Faraoni, V.: Phys. Rev. D 75, 067302 (2007)
Faulkner, T., Tegmark, M., Bunn, E.F., Mao, Y.: Phys. Rev. D 76, 063505 (2007). astro-ph/0612569v1
Felice, A.D., Tsujikawa, S.: Living Rev. Relativ. 13, 3 (2010). 1002.4928v2
Fujii, Y.: Prog. Theor. Phys. 99, 599 (1998). gr-qc/9708010v1
Fujii, Y., Maeda, K.-I.: The Scalar-Tensor: Theory of Gravitation. Cambridge University Press, Cambridge (2004)
Gkigkitzis, I., Haranas, I., Ragos, O.: Phys. Int. 5(1), 103 (2014). 1406.1581v2
Graca Morais, J.P., Bezerra, V.B.: Mod. Phys. Lett. A 27, 1250178 (2012)
Guendelman, E.I., Kaganovich, A.B.: Int. J. Mod. Phys. A 21, 4373 (2006). gr-qc/0603070v1
Haghani, Z., Harko, T., Lobo, F.S.N., Sepangi, H., Shahidi, S.: Phys. Rev. D 88, 044023 (2013). 1304.5957v3
Harko, T., Lobo, S.N., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 84, 024020 (2011). 1104.2669v2
Lee, C.-C., Geng, C.-Q., Yang, L.: Prog. Theor. Phys. 128, 415 (2012). 1201.4546v3
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003). hep-th/0307288v4
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 74, 086005 (2006). hep-th/0608008v3
Nojiri, S., Odintsov, S.D.: Int. J. Mod. Phys. A 4, 115 (2007). hep-th/0601213v5
Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011). 1011.0544v4
Odintsov, S.D., Sáez-Gómez, D.: Phys. Lett. B 725, 4373 (2013). 1304.5411v3
Oikonomou, V.K., Karagiannakis, N.: Study of antigravity in an F(R) model and in Brans-Dicke theory with cosmological constant (2014). 1408.0398v1
Oltean, M., Brandenberger, R.: Cosmological perturbations in antigravity (2014). 1406.7318v1
Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003). astro-ph/0207347v2
Sharif, M., Arif, S.: Mod. Phys. Lett. A 27, 1250138 (2012). 1302.1191v1
Sharif, M., Zubair, M.: J. Cosmol. Astropart. Phys. 1311, 042 (2013)
Sharif, M., Zubair, M.: Astrophys. Space Sci. 349, 457 (2014)
Song, Y.-S., Hu, W., Sawicki, I.: Phys. Rev. D 75, 044004 (2007). astro-ph/0610532v2
Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010). 0805.1726v4
Srivastava, S.K.: Int. J. Mod. Phys. A 22, 1123 (2007)
Starobinsky, A.A.: JETP Lett. 86, 157 (2007). 0706.2041v2
Tsujikawa, S.: Phys. Rev. D 77, 023507 (2008). 0709.1391v2
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Oikonomou, V.K., Karagiannakis, N. Antigravity in F(R) and Brans-Dicke theories. Astrophys Space Sci 354, 583–596 (2014). https://doi.org/10.1007/s10509-014-2103-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-014-2103-8