This article is cited in 5 papers

The linearization method and new classes of exact solutions in cosmology

A. V. Yurov, A. V. Astashenok

Immanuel Kant State University of Russia

Abstract: 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, inflation, exact solution.

Received: 06.01.2008
Revised: 13.03.2008

DOI: 10.4213/tmf6316

 English version: Theoretical and Mathematical Physics, 2009, 158:2, 262–269

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