# Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology

## TL;DR

This paper introduces the use of the minimum spanning tree (MST) to analyze the cosmic web, demonstrating its ability to improve cosmological parameter constraints beyond traditional two-point statistics.

## Contribution

It is the first to utilize the MST for estimating cosmological parameters from simulations, showing it adds valuable information to existing methods.

## Key findings

- MST constraints improve parameter estimation by ~17% on Ω_m and ~12% on A_s.
- Combining MST with power spectrum and bispectrum yields tighter constraints.
- MST can be applied to various current and future galaxy surveys for cosmological analysis.

## Abstract

Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, $N$-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COLA simulations with a box size of $250\ h^{-1}{\rm Mpc}$, varying the amplitude of scalar fluctuations $\left(A_{\rm s}\right)$, matter density $\left(\Omega_{\rm m}\right)$, and neutrino mass $\left(\sum m_{\nu}\right)$. The power spectrum $P$ and bispectrum $B$ are measured for wavenumbers between $0.125$ and $0.5$ $h{\rm Mpc}^{-1}$, while a corresponding lower cut of $\sim12.6$ $h^{-1}{\rm Mpc}$ is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved $1\sigma$ constraints of $\sim 17\%$ ($\sim 12\%$) on $\Omega_{\rm m}$ and $\sim 12\%$ ($\sim 10\%$) on $A_{\rm s}$ with respect to $P$ ($P+B$) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics.