Beyond twopoint statistics: using the Minimum Spanning Tree as a tool for cosmology
Abstract
Cosmological studies of large scale structure have relied on 2point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this 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, which is defined to be the minimum weighted spanning graph. We study the dependence of the MST statistics on cosmological parameters using haloes from a suite of COLA simulations with a box size of $250\ h^{1}{\rm Mpc}$ that vary 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 $P(k)$ and bispectrum $B(k_{1}, k_{2}, k_{3})$ are measured between $k$ $\sim 0.125$ 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 on $\Omega_{\rm m}$ of $\sim 17\%$ with respect to $P(k)$ and $\sim 12\%$ with respect to $P(k)+B(k_{1}, k_{2}, k_{3})$ thus showing the MST is providing additional information not present in the power spectrum and bispectrum. The MST is a tool which can be used to constrain parameters and/or to test systematics in current and future galaxy surveys. This is especially applicable to spectroscopy surveys (BOSS, DESI, Euclid, PSF, WFIRST and 4MOST) where the MST can be applied in 3D comoving coordinates and photometric surveys (DES and LSST) in tomographic shells. The Python code, MiSTree, used to construct the MST and run the analysis, is made publicly available at https://knaidoo29.github.io/mistreedoc/.
 Publication:

arXiv eprints
 Pub Date:
 July 2019
 arXiv:
 arXiv:1907.00989
 Bibcode:
 2019arXiv190700989N
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 19 pages, 14 figures (including 2 page appendix with 2 figures), submitted to MNRAS