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Tracing the high-z cosmic web with Quaia: catalogues of voids and clusters in the quasar distribution

This paper presents the first high-redshift ( $0.8<z<2.2$ ) mapping of the cosmic web using the Quaia quasar dataset to identify over 12,000 voids and 41,000 clusters via the REVOLVER method, demonstrating strong consistency with mock simulations while releasing these catalogues and density field estimates to the public for further cosmological analysis.

Original authors: Nestor Arsenov, Andras Kovacs, Mar Perez Sar, Agnes Sz. Bogdan, Francesco Sinigaglia, Francisco-Shu Kitaura, Ginevra Favole, Lyuba Slavcheva-Mihova

Published 2026-04-06

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CC BY 4.0

Original authors: Nestor Arsenov, Andras Kovacs, Mar Perez Sar, Agnes Sz. Bogdan, Francesco Sinigaglia, Francisco-Shu Kitaura, Ginevra Favole, Lyuba Slavcheva-Mihova

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Universe not as a random scattering of stars, but as a giant, invisible spiderweb stretching across the cosmos. This "cosmic web" is made of dark matter and galaxies, connected by long, thin threads (filaments) and separated by massive, empty bubbles called voids.

For a long time, astronomers have been able to map this web in our "neighborhood" (low redshift), but the deeper, older parts of the Universe (high redshift) have been a bit of a mystery. It's like trying to see the roots of a giant tree from far away; the details get blurry.

This paper is about a team of astronomers using a new, super-powerful telescope dataset called Quaia to finally get a clear look at the cosmic web in that distant, ancient past.

Here is the story of what they did, explained simply:

1. The Problem: Too Few "Streetlights"

To map a city at night, you need streetlights. To map the Universe, you need bright objects to act as markers.

The Challenge: In the distant past (between 0.8 and 2.2 billion years after the Big Bang), there aren't many bright galaxies. It's like trying to map a dark forest with only a few scattered fireflies.
The Solution: They used Quasars. These are the brightest beacons in the Universe—supermassive black holes eating gas and shining like cosmic lighthouses. The Quaia dataset gave them a list of 708,000 of these lighthouses.

2. The Method: The "Voronoi" Map

How do you draw a map when you only have dots? The team used a clever geometric trick called Voronoi tessellation.

The Analogy: Imagine you drop a bunch of pebbles on a muddy field. You want to know which pebble is closest to any given spot. You draw lines around each pebble so that every spot inside a line belongs to that specific pebble.
The Result: If a pebble is surrounded by a huge, empty area, that means the mud is sparse (a Void). If pebbles are crowded together, their areas are tiny, meaning the mud is thick (a Cluster).
The Tool: They used a computer program called REVOLVER (which sounds like a robot, but is actually a code) to do this math for 700,000 points.

3. The Reality Check: The "Fake Universe"

Before trusting their map of the real Universe, they had to make sure their tools worked.

The Analogy: Imagine you are a detective trying to find a hidden treasure. Before you go into the real forest, you create 50 fake forests in a computer. You know exactly where the treasure is in the fake ones. You run your detective tools on the fake forests to see if they find the treasure correctly.
The Result: They ran their analysis on 50 simulated universes (mock catalogues). The results from the real Quaia data matched the fake universes almost perfectly (within 5–10%). This proved their map was accurate and not just a trick of the light.

4. The Discoveries: The Biggest Holes and Hills

What did they find in this ancient cosmic web?

The Voids (The Empty Bubbles): They found 12,820 giant empty spaces. The biggest ones were about 250 million light-years across. That's huge! If you put our entire solar system inside one, you wouldn't even notice it.
The Clusters (The Crowded Cities): They found 41,154 crowded regions where quasars were bunched together. The biggest were about 150 million light-years across.
The "Ultra-Large" Question: Some scientists have wondered if there are structures so big they break the rules of physics (like a "Huge-LQG" that is too big to exist). This paper says: No. The biggest structures they found fit perfectly within the limits of our current understanding of how the Universe works. The cosmic web is weird, but it's not that weird.

5. Why This Matters

Think of this paper as handing out a new, high-resolution atlas of the ancient Universe.

The Gift: The authors didn't just write a paper; they released a "Value-Added Catalogue." This is a public dataset where every single quasar is labeled with its address: "Are you in a crowded city? Are you in a lonely desert? How far are you from the center of the desert?"
The Future: Now, other scientists can use this map to study how black holes behave when they are lonely versus when they are in a crowd. They can also use these voids to test theories about Dark Energy (the force pushing the Universe apart).

In a Nutshell

The team used a massive list of ancient cosmic lighthouses (Quasars) to draw a map of the Universe's skeleton. They used geometry to find the biggest empty bubbles and the biggest crowded cities. They double-checked their work with 50 computer simulations and found that everything matches our current theories. They have now shared this map with the world so everyone can explore the deep, dark corners of the cosmic web.

1. Problem Statement and Motivation

The formation and evolution of the cosmic web are fundamental to cosmology, yet the intermediate redshift regime ( $0.8 < z < 2.2$ ) remains relatively uncharted compared to low-redshift galaxy surveys (e.g., SDSS, DESI).

The Challenge: At these redshifts, galaxy samples are sparse. Quasars (QSOs) offer the brightest tracers of the underlying dark matter distribution but suffer from low spatial density and complex selection functions.
The Goal: To map the large-scale structure (LSS) in this redshift range using the new Quaia quasar catalogue, specifically identifying cosmic voids and superclusters (clusters) to test the concordance $\Lambda$ CDM model, the cosmological principle, and the validity of current structure formation theories.
Specific Context: Previous studies (e.g., eBOSS) had limited sky coverage. This analysis aims to extend the statistical power using the all-sky Quaia dataset and investigate the existence of "ultra-large" structures that might challenge standard cosmology.

2. Methodology

2.1. Data Sources

Observational Data: The Quaia quasar catalogue (Storey-Fisher et al. 2024), a cross-match between Gaia DR3 and WISE.
- Selection: 708,483 quasars selected within $0.8 < z < 2.2$ .
- Sky Coverage: A conservative mask was applied ( $sel\_func > 0.52$ ) to exclude noisy regions near the Galactic plane, resulting in a reliable area of 24,372 deg².
Mock Catalogues: 50 realistic mock catalogues generated using the WebOn code.
- Generation: Full-sky lightcone dark matter fields evolved via the ALPT model.
- Biasing: A non-linear, non-local stochastic parametric Hicobian bias model was calibrated to match Quaia's angular clustering and DESI One-percent Survey data.
- Systematics: Realistic spectrophotometric errors and Quaia selection functions (angular and radial) were injected to mimic observational imperfections.

2.2. Analysis Pipeline

Density Field Reconstruction: The REVOLVER (REal-space VOid Locations from surVEy Reconstruction) code was employed.
- Algorithm: Based on the ZOBOV watershed algorithm using Voronoi tessellation.
- Correction: Voronoi cell volumes were weighted and corrected based on the Quaia selection function (completeness) and redshift distribution ( $N(z)$ ) to account for survey systematics and sparsity.
- Cosmology: Flat $\Lambda$ CDM ( $H_0 = 67.6$ , $\Omega_m = 0.31$ , $\Omega_\Lambda = 0.69$ ).
Structure Identification:
- Voids: Identified as connected regions of under-density (valleys in the density field).
- Clusters: Identified as connected regions of over-density (peaks).
- Edge Flagging: A binary parameter (EdgeFlag) was assigned to structures touching the survey mask boundary to distinguish between real structures and artifacts caused by mask proximity.
Validation: Statistical comparisons (radii, density profiles, redshift distributions) were performed between the Quaia data and the ensemble of 50 mocks.

3. Key Contributions and Deliverables

The paper provides three primary public deliverables:

Local Overdensity Map: An estimation of the local overdensity ( $\rho/\bar{\rho}$ ) at the position of every quasar in the Quaia catalogue.
Void and Cluster Catalogues: A comprehensive list of 12,820 voids and 41,154 clusters, including parameters such as effective radius ( $R_{eff}$ ), minimum/average density fluctuations ( $\delta_{min}, \delta_{avg}$ ), and environmental classification ( $\lambda$ ).
Value-Added Quasar Catalogue: A merged dataset linking individual quasars to their local density, host void/cluster membership, and relative position within the structure ( $R/R_{eff}$ ).

4. Key Results

4.1. Statistical Agreement

Consistency: There is an excellent 5–10% level of agreement between the Quaia observational data and the 50 mock catalogues across all tested metrics (radii, densities, redshift distributions).
Edge Effects: Structures near the survey mask (EdgeFlag=1) show slightly higher noise and distortion, particularly for the largest structures. However, the mocks successfully reproduce these edge effects, validating the simulation pipeline.

4.2. Characteristics of Structures

Counts: Identified 12,820 voids and 41,154 clusters.
Sizes:
- Typical void radius: $R_{eff} \approx 100 \, h^{-1}\text{Mpc}$ .
- Typical cluster radius: $R_{eff} \approx 80 \, h^{-1}\text{Mpc}$ .
- Extremes: The largest voids reach $R_{eff} \approx 250 \, h^{-1}\text{Mpc}$ , and the largest clusters reach $R_{eff} \approx 150 \, h^{-1}\text{Mpc}$ .
Ultra-Large Structures: No evidence was found for "ultra-large" cosmic structures (e.g., Giant Quasar Groups) exceeding the dimensions predicted by the $\Lambda$ CDM mocks. The largest structures observed are consistent with cosmic variance in the standard model.
Density Profiles: Stacked density profiles (using Volume-Weighted Estimator) show smooth, significantly under-dense voids and over-dense clusters. The profiles for "voids-in-voids" vs. "voids-in-clouds" (separated by the $\lambda$ parameter) show clear distinctions and match mock predictions.

4.3. Data Sparsity

The mean particle separation ranges from $\approx 45 \, h^{-1}\text{Mpc}$ at $z \approx 0.8$ to $\approx 63 \, h^{-1}\text{Mpc}$ at $z \approx 2.2$ . Structures smaller than $\approx 2 \times$ the mean separation are considered potentially spurious, though they are included in the catalogue for completeness.

5. Significance and Conclusion

Validation of Quaia: The study confirms that the Quaia quasar catalogue, despite being a sparse tracer, is a robust tool for mapping the high-redshift cosmic web when combined with proper selection function corrections.
Cosmological Constraints: The lack of ultra-large structures supports the validity of the cosmological principle and the standard $\Lambda$ CDM model at scales up to $250 \, h^{-1}\text{Mpc}$ at $z \sim 1.5$ .
Future Applications: The released value-added catalogues enable new cross-correlation studies, such as:
- Void-CMB cross-correlations (ISW effect, CMB lensing).
- Analysis of quasar properties (luminosity, radio loudness) as a function of cosmic environment.
- Testing modified gravity and neutrino mass constraints using high-z void statistics.

In summary, this work represents a significant step forward in high-redshift LSS analysis, providing the first large-scale, statistically validated catalogues of cosmic voids and clusters using the Quaia dataset, fully consistent with $\Lambda$ CDM predictions.