Abstract
In this paper, the algebraic structure and the Poisson’s integral theory of f(R) cosmology are presented. Firstly, the Hamilton canonical equations are derived for the system. Secondly, the contravariant algebraic forms of f(R) cosmology are obtained. Thirdly, the Lie algebraic structure admitted and Poisson’s integral methods are investigated for f(R) cosmology. Further, the first integrals and solution of f(R) cosmology are given. Finally, an example is given to illustrate the results.
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Carroll, S.M.: Rev. Rel. 4 (2001). astro-ph/0004075
Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4, 115 (2007)
Vakili, B.: Phys. Lett. B 664, 16 (2008)
Ray, J.R., Reid, J.L.: Phys. Lett. A 71, 317 (1979)
Reid, J.L., Ray, J.R.: J. Phys. A 15, 2751 (1982)
Lutzky, M.: J. Phys. A 11, 249 (1978)
Lutzky, M.: J. Phys. A 12, 973 (1979)
Burgan, J.R., et al.: Phys. Lett. A 74, 11 (1979)
Zhang, H.B., Chen, L.Q.: J. Phys. Soc. Jpn. 74, 905 (2005)
Ray, J.R.: Phys. Rev. D 20, 2632 (1979)
Korsch, H.J.: Phys. Lett. A 74, 294 (1979)
Kaushal, R.S., Korsch, H.J.: J. Math. Phys. 22, 1904 (1981)
Kaushal, R.S., Mishra, S.C.: J. Math. Phys. 34, 5843 (1993)
Mei, F.X.: Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems. Science Press, Beijing (1999) (in Chinese)
Mei, F.X.: Int. J. Non-Linear Mech. 35, 229 (2000)
Mei, F.X.: ASME Appl. Mech. Rev. 53, 283 (2000)
Wolf, F., Korsch, H.: J. Phys. Rev. A 37, 1934 (1988)
Belmonte-Beitia, J., Pérez-García, V.M., Vekslerchik, V., Torres, P.J.: Phys. Rev. Lett. 98, 064102 (2007)
Camci, U., Kucukakca, Y.: Phys. Rev. D 76, 084023 (2007)
Sanyal, A.K., Modak, B., Rubano, C., Piedipalumbo, E.: Gen. Relativ. Gravit. 37(2), 407 (2005)
Sanyal, A.K., Modak, B.: Class. Quantum Gravity 19, 515 (2002)
Vakili, B.: Phys. Lett. B 669, 206 (2008)
Capozziello, S., Stabile, A., Troisi, A.: Class. Quantum Gravity 24, 2153 (2007)
Fu, J.L., Chen, X.W., Luo, S.K.: Appl. Math. Mech. 20, 1266 (1999)
Liu, H.J., Tang, Y.F., Fu, J.L.: Chin. Phys. 15, 1653 (2006)
Capozziello, S., De Ritis, R., Rubano, C.: Phys. Lett. A 177, 18 (1993)
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This work has been partially supported by the National Natural Science Foundations of China (No. 11072218).
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Fu, JL., Xie, FP. & Guo, YX. Algebraic Structure and Poisson’s Integral Theory of f(R) Cosmology. Int J Theor Phys 51, 35–48 (2012). https://doi.org/10.1007/s10773-011-0875-y
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DOI: https://doi.org/10.1007/s10773-011-0875-y