Abstract
In the present paper, using action derivative with respect to Ricci scalar and its expansion relative to red-shift, to the second-order and consequently without needing dark energy, the history of cosmos expansion is reconstructed in vacuum. Then, employing supernova data, free parameters of the model which are the expansion coefficients, are calculated. It will be seen that if the free parameters of the model are zero, action of general relativity, which is a boundary mode of the gravity, is found. Also the cosmic age for this model in vacuum is calculated. Finally, it is attempted to reconstruct the reference action in terms of its Taylor expansion. Thus, it will be found that the reconstructed action and their actions definitely pass the Solar system tests.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allemandi, G., Borowiec, A., Francaviglia, M.: Phys. Rev. D 70, 103503 (2004)
Amanullah, R., et al.: Astrophys. J. 716, 712 (2010)
Appleby, S.A., Battye, R.A.: Phys. Lett. B 654, 7 (2007)
Asgari, S., Saffari, R.: Appl. Phys. Res. 2, 99 (2010)
Asgari, S., Saffari, R.: Gen. Relativ. Gravit. 44, 737 (2012)
Baghram, S., Rahvar, S.: Phys. Rev. D 80, 124049 (2009)
Bamba, K., et al.: J. Cosmol. Astropart. Phys. 0810, 045 (2008)
Bamba, K., et al.: Astrophys. Space Sci. 342, 155 (2012)
Caldwell, R., Kamionkowski, M.: Annu. Rev. Nucl. Part. Sci. 59, 397 (2009)
Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002)
Capozziello, S., Francaviglia, M.: Gen. Relativ. Gravit. 40, 357 (2008)
Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Int. J. Mod. Phys. D 12, 1969 (2003)
Capozziello, S., Cardone, V.F., Trosi, A.: Phys. Rev. D 71, 043503 (2005)
Capozziello, S., Cardone, V.F., Salzano, V.: Phys. Rev. D 78, 063504 (2008)
Carloni, S., Dunsby, P.K.S., Capozziello, S., Troisi, A.: Class. Quantum Gravity 22, 4839 (2005)
Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.: Phys. Rev. D 70, 043528 (2004)
Chiba, T.: Phys. Lett. B 575, 1 (2003)
Cognola, G., et al.: Phys. Rev. D 77, 046009 (2008)
Cole, S., et al.: Mon. Not. R. Astron. Soc. 362, 505 (2005)
Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006)
Demianski, M., Piedipalumbo, E., Rubano, C., Tortora, C.: Astron. Astrophys. 454, 55 (2006)
Dunlop, J., et al.: Nature 381, 581 (1996)
Eisenstein, D.J., et al.: Astrophys. J. 633, 560 (2005)
Elizade, E., et al.: Phys. Rev. D 83, 086006 (2011)
Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010)
Frieman, J., Turner, M., Huterer, D.: Annu. Rev. Astron. Astrophys. 46, 385 (2008)
Girones, Z., Marchetti, A., Mena, O., Pena-Garay, C., Rius, N.: J. Cosmol. Astropart. Phys. 1011, 004 (2010)
Hashemi, R., Saffari, R.: Planet Space Sci. 59, 338 (2011)
Hu, W., Sawicki, I.: Phys. Rev. D 76, 064004 (2007)
Jain, D., Dev, A.: Phys. Lett. B 633, 436 (2006)
Jain, B., Taylor, A.: Phys. Rev. Lett. 91, 141302 (2003)
Khoury, J., Weltman, A.: Phys. Rev. D 69, 044026 (2004)
Kleinert, H., Schmidt, H.J.: Gen. Relativ. Gravit. 34, 1295 (2002)
Linder, E.V.: Gen. Relativ. Gravit. 40, 329 (2008)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 576, 5 (2003a)
Nojiri, S., Odintsov, S.D.: Mod. Phys. Lett. A 19, 627 (2003b)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003c)
Nojiri, S., Odintsov, S.D.: Gen. Relativ. Gravit. 36, 1765 (2004)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 74, 086005 (2006)
Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4, 115 (2007a)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 652, 343 (2007b)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 657, 238 (2007c)
Nojiri, S., Odintsov, S.D.: J. Phys. Conf. Ser. 66, 012005 (2007d)
Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011)
Nojiri, S., Odintsov, S.D., Saez-Gomez, D.: (2009). arXiv:0908.1269
Olmo, G.J.: Phys. Rev. D 72, 083505 (2005)
Padmanabhan, T.: Phys. Rep. 380, 235 (2003)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Saffari, R., Rahvar, S.: Phys. Rev. D 77, 104028 (2008)
Saffari, R., Rahvar, S.: Mod. Phys. Lett. A 24, 305 (2009)
Sahni, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 9, 373 (2000)
Sami, M.: Curr. Sci. 97, 887 (2009)
Seljak, U., et al.: Phys. Rev. D 71, 103515 (2005)
Silvestri, A., Trodden, M.: Rep. Prog. Phys. 72, 096901 (2009)
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 170, 377 (2007)
Spinrad, H., et al.: Astrophys. J. 484, 581 (1999)
Starobinsky, A.A.: JETP Lett. 86, 157 (2007)
Thakur, S., Sen, A.A., Seshadri, T.R.: Phys. Lett. B 696, 309 (2011)
Tsujikawa, S.: Phys. Rev. D 77, 023507 (2008)
Acknowledgements
We would like to thank anonymous referees for useful comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Masoudi, M., Saffari, R. Vacuum solution of a quadratic red-shift based correction in f(R) gravity. Astrophys Space Sci 346, 559–566 (2013). https://doi.org/10.1007/s10509-013-1477-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-013-1477-3