Geodesic
The linearization method and new classes of exact solutions in cosmology
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 312-320 Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop a method for constructing exact cosmological solutions of the Einstein equations based on representing them as a second-order linear differential equation. In particular, the method allows using an arbitrary known solution to construct a more general solution parameterized by a set of $3N$ constants, where $N$ is an arbitrary natural number. The large number of free parameters may prove useful for constructing a theoretical model that agrees satisfactorily with the results of astronomical observations. Cosmological solutions on the Randall–Sundrum brane have similar properties. We show that three-parameter solutions in the general case already exhibit inflationary regimes. In contrast to previously studied two-parameter solutions, these three-parameter solutions can describe an exit from inflation without a fine tuning of the parameters and also several consecutive inflationary regimes.
Keywords: cosmology
Mots-clés : inflation, exact solution. 
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A. V. Yurov; A. V. Astashenok. The linearization method and new classes of exact solutions in cosmology. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 312-320. http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a9/

[1] V. M. Zhuravlev, S. V. Chervon, V. K. Schigolev, ZhETF, 114:2 (1998), 406–417 | DOI | MR

[2] J. D. Barrow, Phys. Rev. D, 49:6 (1994), 3055–3058 | DOI | MR

[3] R. Maartens, D. R. Taylor, N. Roussos, Phys. Rev. D, 52:6 (1995), 3358–3364 | DOI

[4] G. F. R. Ellis, M. S. Madsen, Class. Quantum Grav., 8:4 (1991), 667–676 | DOI | MR | Zbl

[5] J. E. Lidsey, Class. Quantum Grav., 8:5 (1991), 923–933 | DOI | MR

[6] J. D. Barrow, P. Saich, Class. Quantum Grav., 10:2 (1993), 279–283 | DOI | MR

[7] P. Parson, J. D. Barrow, Class. Quantum Grav., 12:7 (1995), 1715–1721 | DOI | MR | Zbl

[8] A. V. Yurov, Phantom scalar fields result in inflation rather than Big Rip, arXiv: astro-ph/0305019

[9] S. D. Vereschagin, A. V. Yurov, TMF, 139:3 (2004), 405–422 | DOI | MR

[10] A. V. Yurov, V. A. Yurov, Phys. Rev. D, 72:2 (2005), 026003 | DOI | MR

[11] A. V. Yurov, A. V. Astashenok, V. A. Yurov, Gravit. Cosmol., 14:1 (2008), 8–16 | DOI | Zbl

[12] J. Cepa, J. Astron. Astrophys., 422:3 (2004), 831–839 | DOI | Zbl

[13] A. A. Andrianov, F. Cannata, A. Y. Kamenshchik, Phys. Rev. D, 72 (2005), 043531 | DOI

[14] A. V. Yurov, P. M. Moruno P. F. González-Díaz, Nucl. Phys. B, 759:1–2 (2006), 320–341 | DOI | MR | Zbl

[15] E. Elizalde, S. Nojiri, S. Odintsov, Phys. Rev. D, 70:4 (2004), 043539 | DOI

[16] S. Nojiri, S. Odintsov, Phys. Lett. B, 562 (2003), 147–152 | DOI | MR | Zbl