Constraining Cosmology with Big Data Statistics of Cosmological Graphs
  By utilizing large-scale graph analytic tools implemented in the modern Big
Data platform, Apache Spark, we investigate the topological structure of
gravitational clustering in five different universes produced by cosmological
$N$-body simulations with varying parameters: (1) a WMAP 5-year compatible
$\Lambda$CDM cosmology, (2) two different dark energy equation of state
variants, and (3) two different cosmic matter density variants. For the Big
Data calculations, we use a custom build of stand-alone Spark/Hadoop cluster at
Korea Institute for Advanced Study (KIAS) and Dataproc Compute Engine in Google
Cloud Platform (GCP) with the sample size ranging from 7 millions to 200
millions. We find that among the many possible graph-topological measures,
three simple ones: (1) the average of number of neighbors (the so-called
average vertex degree) $\alpha$, (2) closed-to-connected triple fraction (the
so-called transitivity) $\tau_\Delta$, and (3) the cumulative number density
$n_{s\ge5}$ of subcomponents with connected component size $s \ge 5$, can
effectively discriminate among the five model universes. Since these
graph-topological measures are in direct relation with the usual $n$-points
correlation functions of the cosmic density field, graph-topological statistics
powered by Big Data computational infrastructure opens a new, intuitive, and
computationally efficient window into the dark Universe.
