Vacuum Selection from Cosmology on Networks of String Geometries

TL;DR

This paper applies network science to the string landscape, modeling geometries as networks to understand vacuum selection through cosmological dynamics influenced by network eigenvectors.

Contribution

It introduces a novel network-based framework for analyzing the string landscape and identifies a dynamical vacuum selection mechanism via network eigenvectors.

Findings

Network models of string geometries are constructed.

Vacuum selection is governed by the largest eigenvector of a network matrix.

The framework links cosmological dynamics to network spectral properties.

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.