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Dynamics of Bianchi I Elastic Spacetimes

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.
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