Big Data Astronomy: Large-scale Graph Analyses of Five Different Multiverses

By utilizing large-scale graph analytic tools in the modern Big Data platform, Apache Spark, we investigate the topological structures of five different multiverses produced by cosmological n-body simulations with various cosmological initial conditions: (1) one standard universe, (2) two different dark energy states, and (3) two different dark matter densities. For the Big Data calculations, we use a custom build of stand-alone Spark cluster at KIAS and Dataproc Compute Engine in Google Cloud Platform with the sample sizes ranging from 7 millions to 200 millions. Among many graph statistics, we find that three simple graph measurements, denoted by (1) $n_\k$, (2) $\tau_\Delta$, and (3) $n_{S\ge5}$, can efficiently discern different topology in discrete point distributions. We denote this set of three graph diagnostics by kT5+. These kT5+ statistics provide a quick look of various orders of n-points correlation functions in a computationally cheap way: (1) $n = 2$ by $n_k$, (2) $n = 3$ by $\tau_\Delta$, and (3) $n \ge 5$ by $n_{S\ge5}$.