Cosmology and neutrino mass with the minimum spanning tree

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 νΛCDM model. The measurements are made in redshift space using haloes from the Quijote simulation of mass $\ge 3.2\times 10^{13}\, h^{-1}\, {\rm M}_{\odot }$ in a box of length $L_{\rm box}=1\, h^{-1}\, {\rm Gpc}$. The power spectrum multipoles (monopole and quadrupole) are computed for Fourier modes in the range $0.006\, h{\rm Mpc}^{-1} \lt k \lt 0.5\, h{\rm Mpc}^{-1}$. For comparison the MST is measured with a minimum length-scale of $l_{\min }\simeq 13\, h^{-1}\, {\rm Mpc}$. 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_ν and cosmological parameters h, n_s, and Ω_b but the power spectrum alone provides tighter constraints on Ω_m and σ₈. Combined we find constraints that are a factor of two (or greater) on all parameters with respect to the power spectrum (for M_ν 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, Euclid, and Rubin-LSST).