# Navigability of Random Geometric Graphs in the Universe and Other Spacetimes

## TL;DR

This paper investigates the navigability of random geometric graphs in different Lorentzian spacetimes, finding that those in dark energy-dominated universes are as navigable as hyperbolic graphs, linking dark energy to network navigability.

## Contribution

It demonstrates that random geometric graphs in de Sitter spacetimes are navigable, establishing a connection between dark energy presence and graph navigability, which is novel compared to prior hyperbolic models.

## Key findings

- Graphs in dark energy spacetimes are navigable.
- Navigability is absent in matter-only spacetimes.
- Links dark energy to network navigability and cosmological models.

## Abstract

Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de Sitter spacetimes, such as the Lorentzian spacetime of our accelerating universe, are more attractive as their predictions are more consistent with observations in real networks. Yet another important property of hyperbolic graphs is their navigability, and it remains unclear if de Sitter graphs are as navigable as hyperbolic ones. Here we study the navigability of random geometric graphs in three Lorentzian manifolds corresponding to universes filled only with dark energy (de Sitter spacetime), only with matter, and with a mixture of dark energy and matter as in our universe. We find that these graphs are navigable only in the manifolds with dark energy. This result implies that, in terms of navigability, random geometric graphs in asymptotically de Sitter spacetimes are as good as random hyperbolic graphs. It also establishes a connection between the presence of dark energy and navigability of the discretized causal structure of spacetime, which provides a basis for a different approach to the dark energy problem in cosmology.