VERSUS: An excursion-set-inspired void-finder for the Stage-IV era

The paper introduces VERSUS, a fast and user-friendly void-finding algorithm that accurately identifies spherical underdensities and aligns with theoretical excursion set predictions across a wide range of scales, making it well-suited for analyzing data from upcoming Stage-IV cosmological surveys.

The Gist

Imagine the universe as a giant, three-dimensional sponge. Most of the "sponge" material (matter) is clumped together in thick, dense knots (galaxies and clusters) and long, stringy strands (filaments). But the vast majority of the sponge's volume is actually empty space—huge, hollow bubbles where almost nothing exists. Astronomers call these bubbles cosmic voids.

For a long time, measuring these bubbles has been tricky. It's like trying to count the size of holes in a sponge that is constantly changing shape, while looking at it through a foggy window. Different tools (algorithms) used to find these holes often gave different answers, and many required a lot of messy "cleaning up" afterward to make sense of the data.

This paper introduces a new tool called VERSUS. Think of VERSUS as a highly specialized, super-fast "hole-puncher" designed specifically to find these cosmic bubbles in a way that matches our best theoretical predictions.

Here is a simple breakdown of what the paper does:

1. The Problem: The "Foggy Window" and the "Messy Cleanup"

In the past, finding voids was like trying to find the exact center of a bubble in a soap foam using a topological map. The tools would find the bubbles, but they often included the thick, soapy edges, making the bubbles look weirdly shaped or too big. To fix this, scientists had to run a second program to "clean" the list, cutting off the edges and reshaping the bubbles. This was slow, complicated, and sometimes threw away real bubbles by mistake.

2. The Solution: VERSUS (The "Density Scanner")

VERSUS works differently. Instead of mapping the edges of the foam, it scans the density of the "sponge" directly.

• How it works: Imagine you have a grid of tiny cubes covering the universe. VERSUS looks at each cube and asks, "Is this area emptier than a specific threshold?"
• The "Bubble" Logic: If a group of cubes is empty enough, it marks them as a potential bubble.
• The "Merging" Trick: In the real universe, bubbles aren't perfect spheres; they get squashed and stretched. VERSUS allows these bubbles to overlap and merge. If two small empty spots touch, VERSUS combines them into one bigger bubble. This ensures the final size of the bubble matches the total empty space, even if the shape is weird.

3. Why It's Special: "No Cleanup Needed"

The biggest claim of this paper is that VERSUS finds bubbles that already look exactly like the theoretical models predict.

• The Analogy: Imagine a chef (the theory) who predicts exactly how a cake should rise. Old tools (other algorithms) would bake the cake, then have to chop off the burnt edges and reshape it to match the chef's drawing. VERSUS bakes the cake so perfectly that it comes out of the oven looking exactly like the drawing. No chopping required.
• The Result: The authors tested VERSUS on fake data (where they knew the answer beforehand) and on realistic simulations of galaxies. In every case, VERSUS found the bubbles perfectly without needing any post-processing "cleaning."

4. Speed and Efficiency

VERSUS is incredibly fast. The authors compared it to the current standard tool (called VIDE).

• The Analogy: If the old tool was a manual typewriter, VERSUS is a modern word processor. It can process a massive simulation of the universe (containing millions of galaxies) in just a few seconds on a standard computer.
• Why this matters: Because it is so fast, scientists can now run thousands of simulations to test different theories about the universe. This opens the door to using "simulation-based" methods, where computers learn the rules of the universe by playing with millions of fake universes, rather than just guessing.

5. Real-World Testing

The team didn't just test it on perfect, round boxes of data. They also tested it on a "messy" dataset that mimics a real telescope survey (like the BOSS survey), which has holes and irregular shapes because telescopes can't see every part of the sky at once.

• The Result: VERSUS handled the messy, irregular shapes perfectly, proving it is ready to be used on real data from upcoming massive sky surveys (Stage-IV surveys).

Summary

The paper presents VERSUS, a new, fast, and user-friendly computer program that finds cosmic voids (empty spaces in the universe). Unlike older methods that required messy cleanup steps, VERSUS finds bubbles that naturally match our best scientific theories. It is fast enough to handle the massive amounts of data coming from next-generation telescopes, making it a powerful new tool for understanding the structure of the universe.

Technical Summary

Technical Summary: VERSUS – An Excursion-Set-Inspired Void-Finder for the Stage-IV Era

Problem Statement
Cosmic voids serve as unique probes for non-Gaussian information, dark energy, neutrinos, and modified gravity. However, a significant challenge in void cosmology is the mismatch between theoretical predictions and observational measurements. Theoretical models, specifically the excursion set formalism (e.g., the Vdn model), predict the abundance and size distribution of spherical, non-overlapping underdensities based on the linear density field. In contrast, standard topological void-finders (such as VIDE and REVOLVER) identify voids based on watershed algorithms and Voronoi tessellations. These methods often produce non-spherical voids and require extensive post-processing (cleaning and resizing) to approximate the spherical assumptions of theoretical models. Furthermore, existing simulation-based modeling approaches are computationally expensive and scale poorly with the large galaxy counts expected from Stage-IV surveys (e.g., DESI, Euclid). There is a need for a void-finding algorithm that is fast, handles complex survey geometries, and produces a catalogue that directly matches excursion set predictions without requiring aggressive post-processing.

Methodology
The authors present VERSUS (Void Extraction of Real-space Spherical UnderdensitieS), a modular Python package (with C/Cython backends) designed to identify voids satisfying the excursion set criteria.

• Algorithmic Approach: VERSUS operates on a 3D mesh derived from a tracer catalogue (galaxies) and, optionally, a random catalogue to account for survey selection functions. It employs iterative convolutions using Fast Fourier Transforms (FFTs) and a spherical top-hat (STH) kernel to smooth the density field at specific input radii ($R_i$).
• Void Identification: The algorithm scans the smoothed density field for cells where the integrated density contrast ($\delta_{sm}$) falls below a specified threshold ($\Delta_v \approx -0.8$). It iterates from the largest to the smallest input radius.
• Merging and Non-Sphericity: A key feature is the handling of overlapping spheres. Instead of enforcing strict sphericity, VERSUS allows smaller voids to merge with larger overlapping structures based on a user-defined overlap fraction ($f_{mg}$). This allows the algorithm to recover the effective volume of non-spherical voids formed by non-linear evolution while maintaining consistency with the excursion set framework.
• Survey Geometry: For real survey data, VERSUS utilizes a "random" catalogue to map the survey footprint and selection function. It applies a Triangular Shaped Cloud (TSC) interpolation to define survey boundaries and flags cells outside the mask, ensuring accurate density estimation and volume calculation in complex geometries.
• Uncertainty Modeling: The authors derive an analytic expression for the uncertainty in void radius estimation due to tracer shot noise. This "smearing" function allows for the convolution of theoretical predictions with the expected measurement noise, facilitating robust cosmological inference.

Key Contributions

1. Direct Theoretical Match: VERSUS is the first void-finder applied to galaxy distributions that achieves strong agreement with excursion set predictions for the Void Size Function (VSF) across the range $25 < R [h^{-1}\text{Mpc}] < 61$ without requiring post-processing cleaning or resizing.
2. Computational Efficiency: The code is optimized for speed, utilizing OpenMP parallelization. It scales with the number of grid cells ($N_{cells}$) rather than the number of galaxies ($N_{gal}$), making it significantly faster (approx. $8\times$) than VIDE for large Stage-IV mock datasets.
3. Handling of Complex Geometries: The algorithm successfully incorporates complex survey masks and redshift-dependent selection functions via random catalogues, demonstrating readiness for real observational data.
4. Analytic Uncertainty Framework: The paper provides a method to quantify and model the bias introduced by tracer density and binning choices, offering a pathway to incorporate these effects directly into likelihood analyses.

Results
The authors validated VERSUS against two simulation types:

• Synthetic Void Population: Using a uniform distribution of tracers with embedded synthetic voids, VERSUS accurately recovered the true void centers and radii. In contrast, topological algorithms (VIDE and REVOLVER) required aggressive cleaning that removed a significant fraction of genuine voids (over-cleaning) and failed to recover the correct density profiles.
• AbacusSummit HOD Mocks: Applied to a high-fidelity $N$-body simulation populated with realistic galaxies (DESI LRG-like), VERSUS produced a VSF that matched theoretical predictions using a consistent void bias parameter ($b_v \approx 3.2$). Conversely, the cleaned VIDE catalogue required an inconsistent, lower bias parameter ($b_v \approx 2$) to match theory, despite its density profiles suggesting a higher bias.
• Survey Footprint: When applied to a mock with the BOSS DR12 CMASS South Galactic Cap geometry, VERSUS accurately recovered the VSF using a random catalogue to trace the selection function, matching the results from the periodic cubic box.
• Performance: On a $(2 h^{-1}\text{Gpc})^3$ simulation, VERSUS achieved runtimes under 20 seconds (using 16 threads) with a grid resolution of $500^3$ cells, demonstrating suitability for the computational demands of Stage-IV survey analysis.

Significance
The paper claims that VERSUS establishes a novel pathway for unifying analytic and simulation-based approaches to cosmic void cosmology. By generating void catalogues that are self-consistently described by excursion set theory, VERSUS removes the need for ad hoc corrections or unphysical adjustments to bias parameters. Its computational speed enables the use of simulation-based forward modeling (e.g., training emulators or Bayesian inference) on large datasets, which was previously computationally prohibitive. The authors position VERSUS as a robust, user-friendly tool ready for application to real Stage-IV survey data, promising more precise constraints on fundamental physics through void statistics.