Chaos in Bianchi I cosmology

We have investigated the dynamical evolution of the Yang--Mills (YM) field in Bianchi I cosmology background. We find that the long-time evolution behaviour of the YM field is highly sensitive to initial conditions, i.e. small fluctuations of initial conditions for fixed Hamiltonian of the system may rapidly change the evolution of the field. By using the Poincar\'e section method, we further illustrate that the dynamical evolution of the YM field in Bianchi I cosmology background has certain typically chaotic properties.