Qualitative analysis of ten-dimensional lovelock cosmological models

The Einstein-like field equations obtained from the variation of a Lagrangian containing linear, quadratic (Gauss-Bonnet) and quartic terms for a ten-dimensional cosmological model cannot be solved analytically. However, we can reduce them to a system of dynamical equations for the “Hubble parameters”. The study of the mathematical properties of the fixed points of this system gives a qualitative picture of the behaviour of a class of possible solutions. The inclusion of a quartic term generates an extremely rich structure for the corresponding dynamical system. Some solutions are shown to exhibit the interesting property of dimensional reduction, which has been proposed as a possible explanation of the three-dimensional character of our universe.