Dynamical synchronization, the horizon problem, and initial conditions for inflation

We consider the evolution of homogeneous cosmologies towards the future in a dynamical systems formulation. Using a variational equation approach, we show that there is a short period in which transient solutions between the end of a Mixmaster era and a subsequent Friedmannian state exist. Implications about the generic inhomogeneous evolution towards the future, the recollapse problem, the horizon problem, and the initial conditions required for inflation are briefly discussed.