The linearization method and new classes of exact solutions in cosmology
  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
3\textit{N} constants, where \textit{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.
