Perturbations of the Lambda-CDM model in a dynamical systems perspective
  The observational success and simplicity of the $\Lambda$CDM model, and the
explicit analytic perturbations thereof, set the standard for any alternative
cosmology. It therefore serves as a comparison ground and as a test case for
methods which can be extended and applied to other cosmological models. In this
paper we introduce dynamical systems and methods to describe linear scalar and
tensor perturbations of the $\Lambda$CDM model, which serve as pedagogical
examples that show the global illustrative powers of dynamical systems in the
context of cosmological perturbations. We also study the asymptotic properties
of the shear and Weyl tensors and discuss the validity of the perturbations as
approximations to the Einstein field equations. Furthermore, we give a new
approximation for the linear growth rate, $f(z) = \frac{d\ln \delta}{d\ln a} =
\Omega^{\frac{6}{11}}_m - \frac{1}{70}(1-\Omega_m)^{\frac{5}{2}}$, where $z$ is
the cosmological redshift, $\Omega_m=\Omega_m(z)$, while $a$ is the background
scale factor, and show that it is much more accurate than the previous ones in
the literature.
