Multi-tracer mass bias in matched cosmic voids from SDSS DR7 and the ELUCID constrained simulation

Cosmic voids provide a unique environment for studying the relationship between galaxies, subhaloes, and dark matter in the underdense Universe. Using the SDSS galaxy catalogue and the ELUCID constrained simulation, we establish an observationally anchored framework for measuring multi-tracer mass bias within matched cosmic voids. A sample of 102 matched void pairs is constructed to directly compare galaxy, subhalo, and dark matter mass distributions within an observationally constrained realisation of the local Universe. We find that both the galaxy-to-dark matter and subhalo-to-dark matter mass ratios decrease toward void centres, indicating that luminous and halo tracers become increasingly depleted relative to the underlying matter distribution in the deepest underdensities. In contrast, the galaxy-to-subhalo mass ratio exhibits substantially larger statistical uncertainties within the inner void regions (r/Rv ≲ 0.5). By comparing measurements obtained using independent and common coordinate frameworks, we show that coordinate offsets contribute to the observed scatter but cannot fully account for the large uncertainties. The remaining uncertainty primarily arises from the severe scarcity of massive subhaloes (log10 (Msub /h −1 M⊙) ≥ 11.8) within void interiors, which greatly reduces the number of statistically valid measurements near void centres. Our results provide a direct measurement of multi-tracer mass bias in observationally constrained cosmic environments and highlight the fundamental statistical limitations of multi-tracer studies in extreme underdense regions.

Improvements to AI Systems:

1. Uncertainty-Aware Tracer-Density Modeling: Enhance AI systems (e.g., cosmological inference models) to explicitly model and predict the statistical degradation of mass-bias measurements as a function of radial distance from void centers, incorporating the scarcity of massive subhaloes (log10(M sub) ≥ 11.8) as a prior. The improved system can generate calibrated confidence intervals for multi-tracer mass ratios, avoiding overconfident predictions in underdense regions.

2. Coordinate-Offset Correction in Multi-Survey Matching: Develop AI algorithms that automatically detect and correct for systematic coordinate offsets between observational galaxy catalogues (e.g., SDSS) and constrained simulations (e.g., ELUCID) when matching tracers in voids. The improved system can disentangle true astrophysical scatter from alignment errors, producing more accurate void-by-void mass bias estimates.

3. Sparse-Data Imputation for Void Interiors: Implement generative AI (e.g., normalizing flows or diffusion models) trained on the matched void pairs to infer subhalo mass distributions in void centers where direct measurements are statistically invalid. The improved system can synthesize plausible dark-matter and subhalo density profiles, enabling robust extrapolation of mass bias to r/R v < 0.5 despite extreme tracer scarcity.

4. Adaptive Sampling for Multi-Tracer Ratios: Upgrade AI-driven analysis pipelines to dynamically adjust sampling strategies (e.g., radial bin sizes or bootstrap resampling weights) based on local tracer density. The improved system can automatically increase statistical power in void interiors by borrowing information from neighboring voids or using hierarchical Bayesian pooling, reducing the large uncertainties observed in galaxy-to-subhalo ratios.

5. Simulation-to-Observation Transfer Learning: Use the 102 matched void pairs as a training set to teach AI systems to map dark-matter-only simulation outputs to observed galaxy/subhalo distributions in underdense environments. The improved system can then predict multi-tracer mass bias in any new void catalogue without requiring full constrained simulations, accelerating cosmological surveys.

6. Physical Prior Integration for Extreme Environments: Incorporate the finding that galaxy-to-dark matter and subhalo-to-dark matter ratios decrease toward void centers as a physical constraint in AI-based halo occupation models. The improved system can generate more realistic mock galaxy catalogues for void regions, reducing bias in large-scale structure analyses.