Abstract
We examine in this paper the stability analysis in \(f(R,T, R_{\mu\nu }T^{\mu\nu})\) modified gravity, where \(R\) and \(T\) are the Ricci scalar and the trace of the energy-momentum tensor, respectively. By considering the flat Friedmann universe, we obtain the corresponding generalized Friedmann equations and we evaluate the geometrical and matter perturbation functions. The stability is developed using the de Sitter and power-law solutions. We search for application the stability of two particular cases of \(f(R,T, R_{\mu\nu}T^{\mu\nu})\) model by solving numerically the perturbation functions obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ade, P.A.R., et al.: (2013). arXiv:1303.5062 [astro-ph.CO]
Allemandi, G., Borowiec, A., Francaviglia, M.: Phys. Rev. D 70, 103503 (2004)
Allemandi, G., Borowiec, A., Francaviglia, M., Odintsov, S.D.: Phys. Rev. D 72, 063505 (2005)
Alvarenga, F.G., de la Cruz-Dombriz, A., Houndjo, M.J.S., Rodrigues, M.E., Saèz-Gomèz, D.: Phys. Rev. D 87, 103526 (2013a)
Alvarenga, F.G., Houndjo, M.J.S., Monwanou, A.V., Chabi Orou, J.B.: J. Mod. Phys. 04, 130 (2013b)
Amarzguioui, M., Elgaroy, O., Mota, D.F., Multamaki, T.: Astron. Astrophys. 454, 707 (2006)
Amendola, L., Polarski, D., Tsujikawa, S.: (2006). arXiv:astro-ph/0603703
Anderson, L., et al.: Mon. Not. R. Astron. Soc. 428, 1036 (2013)
Baffou, E.H., Kpadonou, A.V., Rodrigues, M.E., Houndjo, M.J.S., Tossa, J.: Astrophys. Space Sci. 356 (2015a)
Baffou, E.H., Houndjo, M.J.S., Rodrigues, M.E., Kpadonou, A.V., Tossa, J.: (2015b). arXiv:1509.06997 [gr-qc]
Baffou, E.H., Houndjo, M.J.S., Rodrigues, M.E., Kpadonou, A.V., Tossa, J.: Phys. Rev. D 92, 084043 (2015c)
Baffou, E.H., Salako, I.G., Houndjo, M.J.S.: (2016). arXiv:1606.05265 [gr-qc]
Bamba, K., Geng, C.Q., Nojiri, S., Odintsov, S.D.: Europhys. Lett. 89, 50003 (2010). arXiv:0909.4397 [hep-th]
Bamba, K., Lopez-Revelles, A., Myrzakulov, R., Odintsov, S.D., Sebastiani, L.: (2012). arXiv:1207.1009 [gr-qc]
Blake, C., et al.: Mon. Not. R. Astron. Soc. 418, 1707 (2011)
Bohmer, C.G., Hollenstein, L., Lobo, F.S.N.: Phys. Rev. D 76, 084005 (2007)
Brevik, I., Nojiri, S., Odintsov, S.D., Saèz-Gomèz, D.: (2010). arXiv:1002.1942 [hep-th]
Capozziello, S., Francaviglia, M.: Gen. Relativ. Gravit. 40, 357 (2008). arXiv:0706.1146 [astro-ph]
Capozziello, S., Cardone, V.F., Francaviglia, M.: Gen. Relativ. Gravit. 38, 711 (2006)
Capozziello, S., De Laurentis, M., Faraoni, V.: (2010). arXiv:0909.4672 [gr-qc]
Cembranos, J.A.R.: Phys. Rev. D 73, 064029 (2006)
Chiba, T.: Phys. Lett. B 575, 1 (2003)
Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Sebastiani, L., Zerbini, S.: (2008). arXiv:0712.4017 [hep-th]
Cognola, G., Elizalde, E., Odintsov, S.D., Tretyakov, P., Zerbini, S.: (2009). arXiv:0810.4989 [gr-qc]
Cole, S., et al.: Mon. Not. R. Astron. Soc. 362, 505 (2005)
De Felice, A., Tsujikawa, S.: Phys. Lett. B 675, 1–8 (2009). arXiv:0810.5712 [hep-th]
de la Cruz-Dombriz, A., Saèz-Gomèz, D.: (2012a). arXiv:1207.2663 [gr-qc]
de la Cruz-Dombriz, A., Saèz-Gomèz, D.: Class. Quantum Gravity 29, 245014 (2012b). arXiv:1112.4481 [gr-qc]
Eisenstein, D.J., et al.: Astrophys. J. 633, 560 (2005)
Erickcek, A.L., Smith, T.L., Kamionkowski, M.: (2006). arXiv:astro-ph/0610483
Farasat, S.M., Jhangeer, A., Bhatti, A.A.: (2012). arXiv:1207.0708 [gr-qc]
Haghani, Z., Harko, T., Lobo, F.S.N., Sepangi, H.R., Shahidi, S.: (2013). arXiv:1304.5957v3 [gr-qc]
Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 84, 024020 (2011). arXiv:1104.2669 [gr-qc]
Hawkins, E., et al.: Mon. Not. R. Astron. Soc. 346, 78 (2003)
Houndjo, M.J.S.: Int. J. Mod. Phys. D 21, 1250003 (2012)
Jain, B., Taylor, A.: Phys. Rev. Lett. 91, 141302 (2003)
Jamil, M., Momeni, D., Ratbay, M.: Chin. Phys. Lett. 29, 109801 (2012a)
Jamil, M., Momeni, D., Muhammad, R., Ratbay, M.: Eur. Phys. J. C 72, 1999 (2012b)
Kainulainen, K., Reijonen, V., Sunhede, D.: (2006). arXiv:gr-qc/0611132
Koivisto, T.: Phys. Rev. D 73, 083517 (2006)
Li, B., Barrow, J.D.: Phys. Rev. D 75, 084010 (2007). arXiv:gr-qc/0701111
Li, B., Chu, M.C.: Phys. Rev. D 74, 104010 (2006). arXiv:astro-ph/0610486
Li, B., Chan, K.C., Chu, M.C.: Phys. Rev. D 76, 024002 (2007). arXiv:astro-ph/0610794
Nojiri, S., Odintsov, S.D.: (2003). arXiv:hep-th/0307288
Nojiri, S., Odintsov, S.D.: (2006a). arXiv:hep-th/0601213
Nojiri, S., Odintsov, S.D.: (2006b). arXiv:hep-th/0608008
Nojiri, S., Odintsov, S.D.: (2007). arXiv:0707.1941 [hep-th]
Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59–144 (2011). arXiv:1011.0544 [gr-qc]
Nojiri, S., Odintsov, S.D., Toporensky, A., Tretyakov, P.: Gen. Relativ. Gravit. 42, 1997 (2010). arXiv:0912.2488 [hep-th]
Odintsov, S.D., Sàez Gomez, D.: (2013). arXiv:1304.5411v3 [gr-qc]
Olmo, G.J.: Phys. Rev. Lett. 98, 061101 (2007)
Padmanabhan, N., et al.: Mon. Not. R. Astron. Soc. 427, 2132 (2012)
Percival, W.J., et al.: Mon. Not. R. Astron. Soc. 401, 2148 (2010)
Perlmutter, S., et al.: Nature 391, 51 (1998)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Shabani, H., Farhoudi, M.: (2013). arXiv:1306.3164v4 [gr-qc]
Shabani, H., Farhoudi, M.: (2014). arXiv:1407.6187v2 [gr-qc]
Sharif, M., Zubair, M.: J. Cosmol. Astropart. Phys. 03, 028 (2012)
Sharif, M., Zubair, M.: (2013a). arXiv:1306.3450v2 [gr-qc]
Sharif, M., Zubair, M.: J. Cosmol. Astropart. Phys. 11, 042 (2013b)
Song, Y.S., Hu, W., Sawicki, I.: Phys. Rev. D 75, 044004 (2007)
Sotiriou, T.P.: Class. Quantum Gravity 23, 1253 (2006)
Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010). arXiv:0805.1726 [gr-qc]
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 170, 377 (2007)
Tegmark, M., et al.: Phys. Rev. D 69, 103501 (2004)
Vollick, D.N.: Phys. Rev. D 68, 063510 (2003)
Acknowledgements
The authors thank Prof. S.D. Odintsov for useful comments and suggestions. E.H. Baffou thanks IMSP for every kind of support during the realization of this work. M.J.S. Houndjo thanks Université de Natitingou.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baffou, E.H., Houndjo, M.J.S. & Tosssa, J. Exploring stable models in \(f(R,T, R_{\mu\nu}T^{\mu\nu})\) gravity. Astrophys Space Sci 361, 376 (2016). https://doi.org/10.1007/s10509-016-2958-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-016-2958-y