Dark Energy Survey Year 3 results: $w$CDM cosmology from simulation-based inference with persistent homology on the sphere

TL;DR

This work pioneers the application of spherical persistent homology to DES Year 3 weak lensing mass maps using the TopoS2 algorithm within a simulation-based (likelihood-free) inference framework. By forward-modeling DES-like simulations (Gower Street) and compressing topological and second-moment statistics with neural networks, the authors infer $w$CDM parameters while rigorously validating against baryonic effects and calibration via coverage tests. The combined Betti-number and second-moment analysis yields $S_8 = 0.821 \pm 0.018$ and $Ω_ ext{m} = 0.304 \pm 0.037$, with a ~30% improvement in the figure of merit over second moments alone and competitive performance against other DES Y3 higher-order statistics. The spherical, curvature-aware approach, along with robust SBI validation, showcases a powerful path toward exploiting non-Gaussian information in upcoming Stage IV surveys.

Abstract

We present cosmological constraints from Dark Energy Survey Year 3 (DES Y3) weak lensing data using persistent homology, a topological data analysis technique that tracks how features like clusters and voids evolve across density thresholds. For the first time, we apply spherical persistent homology to galaxy survey data through the algorithm TopoS2, which is optimized for curved-sky analyses and HEALPix compatibility. Employing a simulation-based inference framework with the Gower Street simulation suite, specifically designed to mimic DES Y3 data properties, we extract topological summary statistics from convergence maps across multiple smoothing scales and redshift bins. After neural network compression of these statistics, we estimate the likelihood function and validate our analysis against baryonic feedback effects, finding minimal biases (under $0.3σ$) in the $Ω_\mathrm{m}-S_8$ plane. Assuming the $w$CDM model, our combined Betti numbers and second moments analysis yields $S_8 = 0.821 \pm 0.018$ and $Ω_\mathrm{m} = 0.304\pm0.037$-constraints 70% tighter than those from cosmic shear two-point statistics in the same parameter plane. Our results demonstrate that topological methods provide a powerful and robust framework for extracting cosmological information, with our spherical methodology readily applicable to upcoming Stage IV wide-field galaxy surveys.

Figures (17)

• Figure 1: Simulation-based inference (SBI) framework for this work.
• Figure 2: Processed DES Y3 convergence maps following the steps (i) to (iii) from Sec. \ref{['sec:processing_maps']}: smoothing and downgrading the map, masking and rescaling it. This plot is showing the data from the highest redshift bin.
• Figure 3: Visualization of a superlevel set. The colorbar represents $\kappa_r$, the rescaled convergence field as defined in Eq. (\ref{['eq:nu']}). The top panel shows regions where $\kappa_r>2$, revealing mostly connected components that correspond to peaks. In the middle panel ($\kappa_r>0$), both connected components and holes are visible. The lower panel ($\kappa_r>-2$) only has holes, corresponding to underdense regions in the density field. This figure depicts the DES Y3 highest redshift bin, smoothed with $\theta_s=221$ arcmin, our largest scale.
• Figure 4: Persistence diagram and (persistent) Betti numbers corresponding to the superlevel set in Fig. \ref{['fig:filtration']}. The connected components ($H_0$ homology group) are represented in orange and the holes ($H_1$) in purple. Note birth $>$ death because we construct the superlevel set beginning at the highest threshold and descend due to its computational advantages. Betti numbers count the points in the persistence diagram within a certain region. For $\nu=2$, we represent such region with a gray shaded box, where 8 points can be counted for $H_0$, matching the $\beta_0 (\nu=2)$ value in the lower panel and the number of connected components in the top panel of Fig. \ref{['fig:filtration']} minus one (the component that is born at the highest threshold never dies and is mapped to the single connected surface when the excursion set is finished). Persistent Betti numbers apply an additional condition that removes less persistent points (those more likely attributable to noise) by requiring that the persistence $p$ (the difference between death and birth) exceeds a threshold. In this work, we use $p>1$, represented by the purple shading in the top panel.
• Figure 5: Persistence diagrams and corresponding Betti numbers (solid lines) and persistent Betti numbers (dashed lines) for the DES Y3 data for all smoothing scales, for the highest redshift bin. Our analysis represents the first multi-scale persistent homology analysis applied to cosmological data.