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Multiprobe cosmology forecasts from halo-occupation-distribution-based forward modeling of galaxy and void statistics

This paper forecasts that combining void and galaxy statistics within a forward modeling framework using a flexible halo occupation distribution model will significantly improve cosmological constraints on $\Omega_m$ and $\sigma_8$ from DESI Year 5 data by breaking degeneracies between cosmology and the galaxy-halo connection.

Original authors: Andrés N. Salcedo, Alice Pisani, Nico Hamaus

Published 2026-08-13

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CC BY 4.0

Original authors: Andrés N. Salcedo, Alice Pisani, Nico Hamaus

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 solid block of stuff, but as a giant, three-dimensional sponge. If you were to zoom out and look at the cosmic sponge, you'd see a web of thick, tangled strands made of galaxies and dark matter, with enormous, empty bubbles in between. These bubbles are called "cosmic voids." While most people look at the stars and galaxies to understand how the universe works, these empty spaces are actually super-sensitive detectors. Think of them like the quiet, empty rooms in a house; if you know how the furniture (galaxies) is arranged around the empty rooms, you can figure out exactly how the house was built and what materials were used.

Scientists have long used the clustering of galaxies—the way they group together like flocks of birds—to map the universe. But there's a tricky part: we don't perfectly understand the "rules" of how galaxies form inside the invisible clouds of dark matter that hold them. It's like trying to guess the recipe of a cake just by looking at the frosting; you might get the flavor right, but you're guessing about the ingredients. This paper tackles a clever solution: instead of guessing, let's look at both the frosting (galaxies) and the empty spaces (voids) at the same time. By combining these two views, we can "self-calibrate" our understanding, figuring out the secret recipe of the universe while simultaneously learning how the galaxies fit into the picture.

The Cosmic Detective Work

In this study, the authors act like cosmic detectives using a powerful time machine called a computer simulation. They didn't just look at real data; they built a massive, virtual universe inside a supercomputer using the "AbacusSummit" suite of simulations. In this virtual world, they played a game of "fill the halos." They took invisible bubbles of dark matter (halos) and filled them with fake galaxies based on a set of rules called the "Halo Occupation Distribution" (HOD). This is like a recipe that says, "If a dark matter cloud is this heavy, put one galaxy in the middle; if it's heavier, add a few more on the sides."

The tricky part is that the recipe has some unknown ingredients, like how sensitive galaxies are to their environment (a concept called "assembly bias"). To solve this, the authors used a "forward modeling" approach. Instead of trying to reverse-engineer the universe from scratch, they started with a guess, ran their simulation, and then asked: "If the universe were made this way, what would the voids and galaxies look like?" They then compared their virtual results to what we expect to see in real data from the Dark Energy Spectroscopic Instrument (DESI), a giant telescope survey that is currently mapping millions of galaxies.

The Big Reveal: Breaking the Ties

The main discovery of this paper is that combining different types of cosmic clues breaks a major "tie" that has been confusing scientists for years. Usually, when scientists try to measure two key numbers—the total amount of matter in the universe ( $\Omega_m$ ) and how "clumpy" the universe is ( $\sigma_8$ )—they get stuck in a loop. It's like trying to figure out if a cake is sweet because of too much sugar or because the oven was too hot; the two effects look the same if you only taste the frosting.

However, the authors found that cosmic voids react to these two numbers in opposite ways. If you change the amount of matter, the voids get bigger or smaller in a specific pattern. If you change the "clumpiness," the pattern changes differently. By combining the "void size function" (counting how many empty bubbles of different sizes exist) with the "void-galaxy cross-correlation" (measuring how galaxies sit around the voids) and the "galaxy auto-correlation" (how galaxies cluster with each other), they could untangle the knot.

The Results: Sharper than Ever

Using their virtual universe and the expected data from DESI's Year 5 release, the authors forecasted how well we can measure the universe. They found that by combining all these probes, they could pin down the amount of matter in the universe ( $\Omega_m$ ) to within 1.5% and the clumpiness ( $\sigma_8$ ) to within 0.8%. That is incredibly precise!

They also tested other scenarios. For instance, they looked at what happens if we add "weak lensing" data (measuring how the empty voids bend light from background galaxies, like a lens). They found that if we combine void counting with weak lensing from future surveys (like the Stage-IV surveys), the precision could get even better, reaching 1.5% for matter and 1.2% for clumpiness.

The paper also explicitly showed that looking at just one type of data isn't enough. If they only used the void sizes, the uncertainty jumped to 5.9% for matter and 15.5% for clumpiness. If they only used galaxy clustering, it was 4.8% and 7.3%. It was only when they combined the voids and the galaxies that the numbers snapped into focus.

Why This Matters

This work suggests that cosmic voids are not just empty backdrops; they are active, powerful tools. The authors demonstrate that we don't need to know the perfect recipe for galaxy formation to understand the universe's shape. Instead, by letting the voids and galaxies "talk" to each other, they can correct for each other's uncertainties. This means that when the real DESI data comes in, we won't just be counting stars; we'll be able to measure the fundamental properties of our universe with a level of sharpness that was previously out of reach, potentially helping to solve mysteries like why the universe is expanding faster than expected or if gravity works differently on the largest scales.

Technical Summary: Multiprobe Cosmology Forecasts from Halo-Occupation-Distribution-Based Forward Modeling of Galaxy and Void Statistics

Problem Statement
Cosmic voids, the large under-dense regions of the cosmic web, are powerful but under-exploited probes of cosmology. While void statistics provide independent constraints on structure growth ( $\Omega_m$ and $\sigma_8$ ) and offer unique sensitivity to neutrino masses, dark energy, and modified gravity, their potential is currently limited by modeling challenges. The primary difficulty lies in the "void-tracer relation": voids are observationally identified within the galaxy distribution, requiring a model to link "true" matter voids to the observed galaxy voids. Standard theoretical approaches often rely on empirical prescriptions or linear theory assumptions that may not fully capture the complexities of the galaxy-halo connection or the selection effects of specific void finders. Furthermore, degeneracies between cosmological parameters and the galaxy-halo connection (specifically the Halo Occupation Distribution, or HOD) often limit the precision of constraints derived from void statistics alone.

Methodology
The authors employ a simulation-based forward modeling approach to address these challenges, utilizing the AbacusSummit suite of cosmological N-body simulations.

Galaxy Modeling: They populate dark matter halos with mock galaxies using an extended Halo Occupation Distribution (HOD) framework. This model includes parameters for central and satellite galaxy occupations ( $\langle N_{cen}|M_h \rangle$ and $\langle N_{sat}|M_h \rangle$ ) and incorporates galaxy assembly bias, where galaxy occupation depends on the large-scale environment (measured by the matter overdensity $\delta^m_8$ ).
Void Identification: Voids are identified in the simulated HOD galaxy distributions using the $V^2$ algorithm (based on the ZOBOW watershed method), which constructs voids from Voronoi tessellations. This ensures the void statistics are consistent with the specific void-finding algorithm used in observational data.
Observables: The study forecasts constraints from a multi-probe data vector measured in a survey mimicking DESI Year 5 (14,000 deg $^2$ $^{2}$ , $0.4 < z < 0.66$ $0.4 < z < 0.66$ ). The observables include:
1. The void size function ( $n_v$ ).
2. The projected void-galaxy cross-correlation function ( $w_{p,vg}$ ).
3. The projected galaxy auto-correlation function ( $w_{p,gg}$ ).
4. The void excess surface density ( $\Delta\Sigma_{vm}$ ) from weak lensing (in specific scenarios).
Forecasting: Fisher matrix forecasts are computed using derivatives of the data vector with respect to cosmological parameters ( $\Omega_m, \sigma_8$ ) and HOD parameters (including assembly bias parameters $Q_{cen}$ and $Q_{sat}$ ). Covariance matrices are estimated numerically using subvolumes of the simulations and a bootstrap method, with boxcar smoothing to mitigate noise.

Key Contributions

Self-Calibration via Forward Modeling: The paper demonstrates that combining void and galaxy statistics within a single HOD-based forward modeling framework allows for the self-calibration of the void-galaxy relation. By modeling the galaxy-halo connection explicitly, the method marginalizes over uncertainties in how galaxies populate halos, breaking degeneracies that plague analyses using galaxy clustering alone.
Breaking Degeneracies: The study shows that the combination of void size function and galaxy clustering breaks the degeneracy between $\Omega_m$ and $\sigma_8$ . This is driven by the unique, size-dependent response of the void size function to $\Omega_m$ (where $\Omega_m$ affects small and large voids in opposite ways), which contrasts with the degeneracy direction of galaxy clustering.
Assembly Bias Constraints: The framework successfully forecasts constraints on galaxy assembly bias parameters ( $Q_{cen}, Q_{sat}$ ), which are typically difficult to constrain with galaxy clustering alone.
Lensing Integration: The paper provides forecasts for combining the void size function with stacked weak lensing signals from Stage-III and Stage-IV surveys (including kinematic lensing scenarios), showing significant complementary power.

Results

DESI-Y5 Forecasts (Galaxy + Void Statistics): For the fiducial scenario combining $n_v$ , $w_{p,vg}$ , and $w_{p,gg}$ , the authors forecast constraints of 1.5% on $\Omega_m$ and 0.8% on $\sigma_8$ . The best-constrained combination is $\sigma_8 \Omega_m^{-0.038}$ , constrained at the 0.8% level.
Degeneracy Breaking: Using only the void size function ( $n_v$ ) yields weaker constraints (5.9% on $\Omega_m$ , 15.5% on $\sigma_8$ ) with significant degeneracies. Using only galaxy clustering ( $w_{p,gg}$ ) yields 4.8% and 7.3%. The combination of $n_v$ and $w_{p,gg}$ alone improves these to 1.9% and 1.1%, demonstrating that the void size function provides crucial orthogonal information.
Void Lensing Forecasts: Combining the void size function with void lensing from a Stage-IV survey (1250 deg $^2$ overlap) improves constraints to 4.8% ( $\Omega_m$ ) and 2.6% ( $\sigma_8$ ). With an optimistic 10,000 deg $^2$ overlap, constraints reach 3.7% on $\Omega_m$ and 1.5% on $\sigma_8$ . Kinematic lensing (KL) scenarios show similar potential, with 2000 deg $^2$ of KL data yielding 4.0% and 1.7% constraints.
Parameter Sensitivity: The analysis reveals that the void size function is highly sensitive to the transition width of the central occupation ( $\sigma_{\log M}$ ) and the minimum halo mass ( $M_{min}$ ), while being relatively insensitive to satellite occupation parameters ( $M_1, \alpha$ ). Conversely, void lensing is primarily sensitive to cosmological parameters and less to HOD details.

Significance and Claims
The paper claims that this approach establishes a robust pathway for using voids as precision cosmological probes. By integrating void statistics with galaxy clustering in a forward-modeling framework, the study demonstrates that:

No Additional Nuisance Cost: Predicting void statistics within an HOD framework does not require additional nuisance parameters beyond those needed for galaxy clustering, making the combination efficient and theoretically consistent.
Systematics Robustness: Because voids are sensitive to distinct systematics compared to galaxy clustering and weak lensing, they offer valuable cross-checks for late-Universe probes, particularly relevant for addressing the $S_8$ tension.
Future Readiness: The methodology is designed to be applicable to upcoming spectroscopic surveys like DESI and weak lensing surveys (e.g., Roman Space Telescope), providing a blueprint for extracting maximal cosmological information from the galaxy-void connection.

The authors note that while their forecasts are based on real-space statistics, the inclusion of redshift-space distortions and Alcock-Paczyński effects in future work could further enhance constraints, though this would require modeling additional nuisance parameters.

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