Inflation expels runaways

We argue that moduli stabilization generically restricts the evolution following transitions between weakly coupled de Sitter vacua and can induce a strong selection bias towards in inflationary cosmologies. The energy density of domain walls between vacua typically destabilizes Kahler moduli and triggers a runaway towards large volume. This decompactification phase can collapse the new de Sitter region unless a minimum amount of inflation occurs after the transition. A stable vacuum transition is guaranteed only if the inflationary expansion generates overlapping past light cones for all observable modes originating from the reheating surface, which leads to an approximately flat and isotropic universe. High scale inflation is vastly favored. Our results point towards a framework for studying parameter fine-tuning and inflationary initial conditions in flux compactifications.