DYNAMIC DIMENSIONAL REDUCTION INDUCED BY CHANGING EQUATION OF STATE

We study the dynamics of a homogeneous but in general anisotropic multidimensional cosmological model assuming that space-time is a product of a physical space-time M and a compact space B. We take the energy-momentum tensor in the form of a perfect fluid allowing, however, anisotropic pressure. In this case the Einstein field equations can be reduced to a two-dimensional dynamical system. We discuss the general behavior of this dynamical system and investigate conditions under which dynamical dimensional reduction takes place. We also discuss the dynamics of our model when the equation of state of matter is allowed to change. We consider slow and fast changes of the equation of state. In both cases, when the final equation of state is appropriate, the dynamical dimensional reduction takes place. It turns out that slow changes of the equation of state for a certain open set of initial conditions always create inflation in the final state. Rapid changes of the equation of state always suppress inflation if it existed in the initial state. © 1990 The American Physical Society.