Understanding the asymptotic dynamics of the space-time is one of the main goals of theoretical cosmology. In
the context of homogeneous cosmological models, where the Einstein
equations of general relativity reduce to a system of ordinary
differential equations, our knowledge on this problem has increased
substantially over the years, thanks to the application of methods from
the theory of (finite dimensional) dynamical systems. After reviewing
some results on the dynamics of Bianchi I perfect fluid cosmological
models, this talk will focus on the more complicated case of a
space-time filled with an elastic material. In the latter case a
completely new behavior for Bianchi type I solutions is found in the
limit toward the initial (big-bang) singularity, namely the existence
of oscillations between different types of vacuum solutions. This
behavior is associated to energy condition violation as the singularity is approached.
This talk is based on a joint work with Mark Heinzle. |