Abstract
We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence of matter in the form of a perfect fluid, which is necessary for invisibility of extra dimensions that inevitably emerge in the Lovelock theory. In particular, the Jacobs solution has been generalized to an arbitrary order of the theory, and in the third order, an anisotropic exponential solution has been found.
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D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12, 498 (1971).
N. Deruelle. On the approach to the cosmological singularity in quadratic theories of gravity: The Kasner regimes, Nucl. Phys. B 327, 253 (1989).
A. Toporensky and P. Tretyakov, Power-law anisotropic cosmological solution in 5+1 dimensional Gauss-Bonnet gravity, Grav. Cosmol. 13, 207 (2007); arXiv: 0705.1346.
I. V. Kirnos, Anisotropic cosmological solutions of exponential and power-law forms in Gauss-Bonnet theory with matter in Bianchi-type I spaces of arbitrary dimension, In: Proc. of the 2nd Russian School “Modern Theoretical Problems of Gravitation and Cosmology”—GRACOS-2009, 24–29 August 2009, Kazan-Yal’chik (Foliant, Kazan, 2009), pp. 93–98.
I. V. Kirnos, A. N. Makarenko, S. A. Pavluchenko, and A. V. Toporensky, The nature of singularity in multidimensional anisotropic Gauss-Bonnet cosmology with a perfect fluid, Gen. Rel. Grav. 42, 2633 (2010).
S. A. Pavluchenko. The dynamics of the flat anisotropic models in the Lovelock gravity. I: The even-dimensional case. Phys. Rev. D 82, 104021 (2010); arXiv: 1003.4892.
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Talk given at the International Conference RUSGRAV-14, June 27–July 4, 2011, Ulyanovsk, Russia.
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Kirnos, I.V. Some cosmological solutions in an arbitrary order of Lovelock gravity. Gravit. Cosmol. 18, 259–261 (2012). https://doi.org/10.1134/S0202289312040068
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DOI: https://doi.org/10.1134/S0202289312040068