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Cosmological constraints from galaxy clustering and galaxy-galaxy lensing with extended SubHalo Abundance Matching

This paper presents the first cosmological constraints derived from a joint analysis of galaxy clustering and galaxy-galaxy lensing using extended SubHalo Abundance Matching (SHAMe) on GAMA and KiDS-1000 data, yielding an $S_8$ value consistent with Planck results and demonstrating the method's ability to recover input cosmology in simulations while achieving tighter constraints when including small scales.

Original authors: Constance Mahony, Sergio Contreras, Raul E. Angulo, David Alonso, Christos Georgiou, Andrej Dvornik

Published 2026-03-27

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CC BY 4.0

Original authors: Constance Mahony, Sergio Contreras, Raul E. Angulo, David Alonso, Christos Georgiou, Andrej Dvornik

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 as a giant, invisible ocean. In this ocean, there are two main ingredients: dark matter (the invisible water that makes up most of the ocean) and galaxies (the colorful fish swimming in it).

For decades, scientists have been trying to figure out exactly how much dark matter there is and how "clumpy" the ocean is. They have two main ways of looking at this:

The Baby Picture: Looking at the Cosmic Microwave Background (CMB), which is like a baby photo of the universe taken 13.8 billion years ago. This tells us what the universe should look like today if our physics rules are correct.
The Adult Picture: Looking at the actual galaxies and how they are clustered together today.

The Problem:
Recently, scientists noticed a mismatch. The "Baby Picture" (from the Planck satellite) predicts a universe that is slightly clumpier than the "Adult Picture" (from galaxy surveys) actually appears to be. This is called the $S_8$ tension. It's like looking at a blueprint of a house and then looking at the built house, only to realize the walls are slightly thinner than the blueprint said they would be.

The New Approach: The "Galaxy Translator"
This paper introduces a new method called SHAMe (SubHalo Abundance Matching).

Think of dark matter as a collection of invisible, ghostly bubbles (halos) floating in space. Galaxies live inside these bubbles. The problem is, we can't see the bubbles; we can only see the galaxies.

Old Methods: Scientists used to guess how galaxies fit into these bubbles using a lot of complicated rules and many "knobs" to turn. It was like trying to tune a radio with 50 dials, hoping to find the right station.
The SHAMe Method: This new method is like a translator. It says, "If a ghostly bubble is this heavy, it must host a galaxy of this brightness." It uses a computer simulation to map the invisible bubbles to the visible galaxies. The beauty of SHAMe is that it only needs 5 knobs to tune, making it much simpler and more precise than the old methods.

What They Did
The team took data from two major sky surveys:

GAMA: A map of where galaxies are located (clustering).
KiDS-1000: A map of how those galaxies bend light from background objects (lensing).

They fed this data into their "Translator" (the SHAMe emulator) to see if they could figure out the true nature of the universe.

The Results

The Baby Picture Wins (Sort of): When they analyzed the data carefully, avoiding the very small, messy scales where normal matter (gas and stars) gets complicated, they found a value for the universe's clumpiness ( $S_8$ ) that matches the "Baby Picture" (Planck) very well. The tension is gone!
The "All-Scale" Surprise: They also tried looking at every scale, including the tiny, messy ones where gas and stars interact (baryonic effects). Usually, scientists think these interactions smooth things out, making the universe look less clumpy. But surprisingly, when they included these tiny scales, their result actually moved closer to the "Baby Picture" prediction, suggesting the universe might be even clumpier than they thought. This was a happy accident that defied their expectations.
Cracking the Code: Because their method is so precise, they didn't just measure the universe's shape; they also figured out the specific rules of how galaxies form and evolve inside those dark matter bubbles.

Why This Matters
This paper is a big deal because it shows that we don't need to throw away data to get accurate answers. By using a smarter "translator" (SHAMe), we can use more of the universe's information to get a clearer picture.

It's like finally finding the right pair of glasses. Before, the universe looked blurry and contradictory. Now, with this new method, the picture is sharp, and the "Baby" and "Adult" versions of the universe are finally agreeing with each other. This gives us great confidence as we prepare to look at even deeper, larger maps of the universe coming from future telescopes like Euclid and the Rubin Observatory.

1. Problem Statement

Imaging galaxy surveys have become competitive with Cosmic Microwave Background (CMB) experiments in constraining cosmological parameters, specifically the matter density ( $\Omega_m$ ) and the amplitude of matter fluctuations ( $S_8 \equiv \sigma_8 \sqrt{\Omega_m/0.3}$ ). However, a persistent tension exists between $S_8$ values derived from large-scale structure (LSS) surveys and those from the Planck CMB data.

A major source of uncertainty lies in modeling observables on small scales (non-linear regime), where the relationship between galaxies and dark matter halos is complex, non-linear, and influenced by baryonic physics (e.g., feedback).

Current Limitations: Conservative approaches often apply "scale cuts" (discarding small-scale data) to avoid modeling uncertainties, but this discards valuable information.
Modeling Gaps: Traditional Halo Occupation Distribution (HOD) models often require many parameters and struggle to account for assembly bias (the dependence of galaxy clustering on halo formation history). SubHalo Abundance Matching (SHAM) offers a physically motivated alternative with fewer parameters and built-in assembly bias, but it has historically been computationally expensive and rarely used for joint cosmological constraints due to the need for subhalo catalogs.

2. Methodology

The authors present the first joint cosmological analysis of galaxy clustering and galaxy-galaxy lensing using an extended SubHalo Abundance Matching (SHAMe) framework.

A. The SHAMe Model

The authors utilize an extended SHAM model (SHAMe) that connects dark matter subhalos to galaxies using 5 free parameters:

$\sigma$ : Scatter between the peak circular velocity of a subhalo ( $V_{peak}$ ) and the stellar mass ( $M_*$ ) of the galaxy.
$t_{merger}$ : Regulates the removal of "orphan galaxies" (galaxies whose host subhalos fell below simulation resolution).
$f_{k,c+s}$ and $f_{k,c-s}$ : Parameters controlling galaxy assembly bias for central and satellite galaxies, re-ordering the $V_{peak}$ - $M_*$ relation based on linear bias.
$\beta$ : Sets the timescale for satellite galaxy survival within host halos.

B. Emulator Construction

To overcome the computational cost of running full hydrodynamic simulations for every cosmological parameter set, the authors built a neural network emulator:

Training Data: Generated from five gravity-only $N$ -body simulations (TNG300 volume) scaled to 10,000 distinct cosmologies using the Angulo & White (2010) scaling technique.
Mock Generation: Each scaled snapshot was populated with SHAMe mocks.
Architecture: A feed-forward neural network (2 hidden layers, 200 neurons each) trained to predict the projected correlation function ( $w_p$ ) and excess surface density ( $\Delta\Sigma$ ) as a function of cosmological parameters, SHAMe parameters, redshift, and number density.
Efficiency: Evaluation takes ~40ms per sample, enabling rapid likelihood exploration.

C. Data Sets

Galaxy Clustering: Projected correlation function ( $w_p$ ) from the GAMA survey (spectroscopic, high completeness).
Galaxy-Galaxy Lensing: Excess surface density ( $\Delta\Sigma$ ) from KiDS-1000 (weak lensing).
Sample: Four stellar mass bins ( $9.95 < \log(M_*/h^{-2}M_\odot) \leq 11.3$ ).
Likelihood: Gaussian likelihood comparing data vectors to emulator predictions, using a covariance matrix derived from analytic methods (KiDS) and jackknife resampling (GAMA).

D. Analysis Strategies

Fiducial Analysis: Includes all scales for $w_p$ but imposes a scale cut on $\Delta\Sigma$ ( $r_p > 1.4 \, h^{-1}\text{Mpc}$ ) to avoid unmodeled baryonic effects.
All-Scale Analysis: Includes all scales of $\Delta\Sigma$ (down to $r_p < 1.4 \, h^{-1}\text{Mpc}$ ) to test the impact of small-scale data and potential gains in constraining power.

3. Key Contributions

First SHAMe Cosmological Constraints: Demonstrates the viability of SHAMe for joint constraints on cosmological and galaxy-halo connection parameters.
Emulator Development: Successfully built a fast, accurate emulator for SHAMe observables across a wide range of cosmologies and SHAMe parameters.
Validation: Validated the methodology against TNG300 hydrodynamic simulations, showing the ability to recover input cosmology within $1\sigma$ for both fiducial and all-scale analyses.
Assembly Bias Quantification: Successfully constrained assembly bias parameters directly from observational data, showing evidence for strong assembly bias in both central and satellite populations.

4. Results

Cosmological Constraints

Fiducial Result ( $r_p > 1.4$ ):
- $S_8 = 0.793^{+0.025}_{-0.024}$
- $\Omega_m = 0.260^{+0.027}_{-0.015}$
- Significance: Consistent with Planck CMB results at 1.7 $\sigma$ .
All-Scale Result (No scale cuts):
- $S_8 = 0.817^{+0.020}_{-0.019}$
- $\Omega_m = 0.279^{+0.017}_{-0.013}$
- Significance: Consistent with Planck at 0.9 $\sigma$ .
- Improvement: The all-scale analysis yields 21% tighter constraints on $S_8$ and 29% tighter constraints on $\Omega_m$ compared to the fiducial analysis.

Counter-Intuitive Finding

Typically, unmodeled baryonic feedback suppresses small-scale power, leading to lower inferred $S_8$ values. However, including small scales in this analysis increased the inferred $S_8$ value (moving it closer to Planck). The authors suggest this may imply that gas ejection is less efficient in the specific halo mass range probed ( $10^{11.5} - 10^{13} h^{-1}M_\odot$ ) or that the SHAMe model's flexibility compensates for missing physics.

SHAMe Parameters

All 5 SHAMe parameters were constrained simultaneously.
Assembly Bias: The parameters $f_{k,c+s}$ and $f_{k,c-s}$ were found to be positive, indicating a strong positive correlation between large-scale linear bias and galaxy stellar mass/luminosity.
Synergy: While $\Delta\Sigma$ alone constrains only $\sigma$ and $\beta$ , the joint analysis ( $w_p + \Delta\Sigma$ ) constrains all SHAMe parameters and cosmology, highlighting the power of the 2x2pt approach.

5. Significance

Resolving Tension: The results show that joint small-scale analyses using SHAMe can produce $S_8$ constraints that are highly consistent with Planck, potentially alleviating the "S8 tension" without requiring new physics beyond $\Lambda$ CDM.
Efficiency: The work demonstrates that SHAMe, when combined with emulation, is a computationally efficient alternative to complex HOD models or full hydrodynamic simulations for cosmological inference.
Future Prospects: The methodology is well-suited for next-generation surveys like Euclid and LSST, which will provide vast amounts of small-scale data. The ability to constrain assembly bias and cosmology simultaneously makes SHAMe a powerful tool for understanding galaxy formation and the nature of dark energy.

In conclusion, this paper establishes SHAMe as a robust, competitive framework for extracting cosmological parameters from galaxy clustering and lensing, successfully recovering input cosmologies in simulations and providing tight, Planck-consistent constraints on real data.