How massive neutrinos reshape the cosmic web

Technical Summary: How Massive Neutrinos Reshape the Cosmic Web

Problem and Motivation
Current cosmological constraints on the sum of neutrino masses ($M_\nu$) rely heavily on two-point statistics, such as the power spectrum and two-point correlation functions (2PCF). While effective for the early, Gaussian universe, these methods struggle to capture the highly non-Gaussian information inherent in the late-time cosmic web. Furthermore, the suppression of the matter power spectrum caused by massive neutrinos is qualitatively similar to the suppression caused by baryonic feedback (e.g., AGN feedback), creating a degeneracy that limits the precision of neutrino mass measurements. There is a need for statistical methods capable of extracting higher-order structural information to break these degeneracies and distinguish between neutrino effects and baryonic physics.

Methodology
The authors utilize the FLAMINGO suite of hydrodynamical simulations, which include both dark-matter-only plus neutrino (DMO+$\nu$) and full hydrodynamical (HYDRO) runs. The simulations employ a box size of $L_{\text{box}} = 1$ Gpc and model three distinct neutrino masses: 0.06 eV, 0.24 eV, and 0.48 eV. The study focuses on the following methodological components:

1. Cosmic Web Classification: The authors employ the NEXUS+ algorithm to classify the cosmic web into four environments: voids, sheets (walls), filaments, and clusters. This method utilizes the Hessian matrix of the density field across multiple smoothing scales ($R_n = (\sqrt{2})^n R_0$, where $R_0 = 1$ Mpc/$h$). To handle the density field resolution, a cloud-in-cell particle mesh assignment scheme is used, with logarithmic smoothing applied for filament and wall detection to preserve structure in low-density regions.
2. Minimum Spanning Tree (MST) Construction: MST graphs are constructed using 500,000 randomly selected subhaloes with a mass cut of $10^{12} M_\odot$. This mass cut ensures the tracer density matches that expected for DESI-like observations and removes sensitivity to particle mass resolution differences between DMO and HYDRO simulations. The MST statistics analyzed include degree, edge length, branch length, and branch shape.
3. Error Estimation: Statistical errors are estimated using a cross-validation jackknife resampling technique, partitioning the simulation box into $5^3$ sub-boxes.
4. Edge Mapping: To determine the cosmic web environment of MST edges, each edge is subdivided into segments based on the longest edge in the tree relative to the NEXUS+ resolution. This allows for the assignment of fractional weights to different environments (voids, sheets, filaments, clusters) traversed by a single edge.

Key Results

• Impact on Cosmic Web Volume and Density: Increasing the neutrino mass leads to a suppression of structure formation. This manifests as a decrease in the volume and mass fractions occupied by clusters and voids, while the volume fraction of filaments and sheets increases. The volume-weighted density distribution shifts toward higher densities and becomes narrower, indicating that massive neutrinos delay structure formation, resulting in less deep voids and less dense clusters.
• MST Edge Distribution: Approximately 70% of all MST edges lie within filamentary environments across all simulations. This high concentration suggests the MST is intrinsically sensitive to filamentary structures. The remaining edges are distributed among sheets, voids, and clusters, with a clear hierarchy: shorter edges are associated with clusters and filaments, while longer edges correspond to sheets and voids.
• Neutrino vs. Baryonic Signatures: The MST edge length distribution exhibits distinct signatures for neutrino mass and baryonic physics:
  • Neutrinos: Increasing $M_\nu$ decreases the number of edges at small scales ($l \approx 1$ Mpc, associated with clusters/sheets), increases edges at intermediate scales ($l \approx 3$ Mpc, associated with filaments), and decreases edges at large scales ($l \approx 9$ Mpc, associated with voids).
  • Baryons: Baryonic physics increases the number of edges at the smallest scales ($l \approx 1$ Mpc), showing an opposite trend to neutrinos at these scales.
• Environmental Sensitivity: The changes in MST statistics can be directly linked to specific environments. The reduction in small-scale edges is driven by the suppression of cluster formation; the increase at intermediate scales is driven by the expansion of filamentary structures; and the reduction at large scales is linked to the "washing out" of voids (making them shallower and less empty).

Significance and Claims
The paper claims that the Minimum Spanning Tree is a powerful tool for characterizing the cosmic web beyond two-point statistics. Its primary significance lies in its ability to:

1. Break Degeneracies: The MST provides distinct signatures for massive neutrinos and baryonic feedback, particularly in the edge length distribution at small scales, offering a potential avenue to disentangle these effects where traditional power spectrum analyses fail.
2. Trace Filaments: The MST's strong correlation with filamentary environments (holding ~70% of edges) explains its sensitivity to neutrino mass, as neutrinos specifically wash out filamentary structures.
3. Future Application: While the current analysis is performed in 3D space using true subhalo positions (ignoring redshift space distortions), the results motivate the application of MST statistics to real observational data from surveys like DESI and Euclid to improve constraints on neutrino mass and cosmological parameters.

The authors note that the neutrino masses used (up to 0.48 eV) are higher than current observational upper limits, serving to exaggerate effects for study purposes. They acknowledge that distinguishing these effects at lower, realistic mass scales will require further statistical power and the development of methods to account for observational systematics.