Geodesic
The~linearization method and new classes of exact solutions in cosmology
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 312-320

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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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     author = {A. V. Yurov and A. V. Astashenok},
     title = {The~linearization method and new classes of exact solutions in cosmology},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {312--320},
     publisher = {mathdoc},
     volume = {158},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a9/}
}
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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/