Vacuum Selection from Cosmology on Networks of String Geometries

Abstract

We introduce network science as a framework for studying the string landscape. Two large networks of string geometries are constructed, where nodes are extra-dimensional six-manifolds and edges represent topological transitions between them. We show that a standard bubble cosmology model on the networks has late-time behavior determined by the largest eigenvector of $-(\mathbf{L} + \mathbf{D})$, where $\mathbf{L}$ and $\mathbf{D}$ are the Laplacian and degree matrices of the networks, which provides a dynamical mechanism for vacuum selection in the string landscape.