Cosmology and neutrino mass with the Minimum Spanning Tree

Abstract

The information content of the minimum spanning tree (MST), used to capture higher-order statistics and information from the cosmic web, is compared to that of the power spectrum for a $\nu \Lambda$CDM model. The measurements are made in redshift space using haloes from the Quijote simulation of mass $\ge 3.2\times 10^{13}{h}^{-1}{\mathrm{M}}_{\odot }$ in a box of length $L_{\mathrm{box}}=1h^{-1}\mathrm{Gpc}$. The power spectrum multipoles (monopole and quadrupole) are computed for Fourier modes in the range $0.006<k<0.5h{\mathrm{Mpc}}^{-1}$. For comparison the MST is measured with a minimum length scale of $l_{\min }\simeq 13h^{-1}\mathrm{Mpc}$. Combining the MST and power spectrum allows for many of the individual degeneracies to be broken; on its own the MST provides tighter constraints on the sum of neutrino masses $M_{\nu }$ and cosmological parameters $h$, $n_{\mathrm{s}}$, and ${\Omega }_{\mathrm{b}}$ but the power spectrum alone provides tighter constraints on ${\Omega }_{\mathrm{m}}$ and ${\sigma }_8$. Combined we find constraints that are a factor of two (or greater) on all parameters with respect to the power spectrum (for $M_{\nu }$ there is a factor of four improvement). These improvements appear to be driven by the MST's sensitivity to small scale clustering, where the effect of neutrino free-streaming becomes relevant, and high-order statistical information in the cosmic web. The MST is shown to be a powerful tool for cosmology and neutrino mass studies, and therefore could play a pivotal role in ongoing and future galaxy redshift surveys (such as DES, DESI, \emph{Euclid}, and Rubin-LSST).

15 pages, 5 figures (+6 in appendix), accepted for publication in MNRAS

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