We study the cosmological information contained in the cosmic web, categorized as four structure types: nodes, filaments, walls, and voids, using the Quijote simulations and a modified nexus+ algorithm. We show that splitting the density field by the four structure types and combining the power spectrum in each provides much tighter constraints on cosmological parameters than using the power spectrum without splitting. We show the rich information contained in the cosmic web structures—related to the Hessian of the density field—for measuring all of the cosmological parameters, and in particular for constraining neutrino mass. We study the constraints as a function of Fourier scale, configuration space smoothing scale, and the underlying field. For the matter field with $k_{\max }=0.5h/\mathrm{Mpc}$, we find a factor of $\times 20$ tighter constraints on neutrino mass when using smoothing scales larger than $12.5\mathrm{Mpc}/h$, and $\times 80$ tighter when using smoothing scales down to $1.95\mathrm{Mpc}/h$. However, for the $\mathrm{CDM}+\mathrm{baryon}$ field we observe a more modest $\times 1.7$ or $\times 3.6$ improvement, for large and small smoothing scales respectively. We release our new python package for identifying cosmic structures pycosmmommf to enable future studies of the cosmological information of the cosmic web.

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• Cosmology
• Dark matter
• Evolution of the Universe
• Large scale structure of the Universe
• Neutrinos