Inhomogeneous initial conditions for inflation

We address the question whether the inflationary paradigm frees cosmology from the worry about initial conditions. That is, we study the influence of initial inhomogeneities on the inflationary epoch. We derive a simple set of approximate equations and use it to illustrate some features of deviations from homogeneity. However, the approximation methods are limited and in order to explore the full effect of initial inhomogeneities we turn to numerical calculations. The picture that emerges from these calculations is that inhomogeneities can prohibit ``new'' inflation from taking place. The crucial feature necessary for ``chaotic'' inflation is a sufficient high average field over a region of several horizon sizes.