Modeling in chaotic relativity

The chaotic behavior of solutions to Einstein's equations has recently been studied by Barrow within the framework of the dynamical systems theory. Barrow's program of gravitational turbulence is implemented in part by considering the solutions of type ${\mathrm{VII}}_0$ and IX as well as some intermediate types. Quantitative measures of chaos, such as the power spectrum and Lyapunov characteristic exponent, are computed. By converting the equations of motion for the cosmic scale factors to stochastic Langevin's equations, the Mixmaster cosmology in the presence of driving noise terms is investigated. Possible sources of noise can be attributed to an imperfect cancellation of the effective vacuum energy density and the energy density associated with the Higgs field. An ensemble average over random trajectories leads to the suppression of chaotic behavior for type-IX cosmology.