Galaxy clustering in modified gravity from full-physics simulations. I: two-point correlation functions

The following is a detailed summary of the scientific paper, extracted directly from the text:

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We present an in-depth investigation of galaxy clustering based on a new suite of realistic large-box galaxy-formation simulations in f(R) gravity, with a subgrid physics model that has been recalibrated to reproduce various observed stellar and gas properties. We focus on the two-point correlation functions of the luminous red galaxies (LRGs) and emission line galaxies (ELGs), which are primary targets of ongoing and future galaxy surveys such as DESI.

The investigation reveals several surprising results regarding the influence of modified gravity (MG) on matter clustering and the galaxy-halo connection. One finding is that, due to nontrivial effects of modified gravity, the clustering signal does not depend monotonically on the fifth-force strength.

Findings for Emission Line Galaxies (ELGs):

For ELGs, the behavior can be explained by the time evolution of the fifth force, which allows weaker f(R) models to display nearly the same—up to 25%—deviations from CDM as the strongest ones, albeit at lower redshifts. This implies that even very weak f(R) models can be strongly constrained.

Findings for Luminous Red Galaxies (LRGs):

For LRGs, this complex behavior presents a challenge: this complicated behaviour poses a challenge to meaningfully constraining this model.

General Systemic Findings:

The study demonstrates that galaxy formation acquires a significant environment dependence in f(R) gravity which, if not properly accounted for, may lead to biased constraints on the model.

Halo Mass Function (HMF) Analysis:

In the analysis of the differential HMF (dn/d log M), we observe that:

1. we see a 'bump' in the HMF enhancement which peaks within some mass range.

2. we note from Fig. 3 that different models have similarly shaped excesses... it seems that weaker MG models display the same deviations from GR as stronger ones, except that they do so at lower redshift. In essence, MG models—at least those that are similar to the f(R) gravity model—with varying strengths can be thought of as delayed versions of one another.

3. We observed a saturation effect where, for instance, F4.0 and F4.5 HMFs appear to be practically coinciding... if this happens before the period when haloes experience most of their growth, then the effect simply would not be reflected in the halo growth.

Clustering Results (Real-Space Correlation Functions):

• ELGs: The real-space correlation functions show significant deviations. For instance, in F5.5 at z = 1.155, F6.0 and F5.5 at z = 0.652 and F4.0, F4.5 and F6.0 at z = 0.155 we note particularly large deviations of 20 - 30% below GR at r 5 Mpc. The behavior is non-monotonic with respect to the fifth-force strength, but the time evolution is a key factor.

• LRGs: The deviations in LRG CFs are smaller. The deviations in the LRG CFs for the MG models from GR are at most on the 10% level. The results show that F6.0 has nearly identical LRG clustering to GR because the fifth force in this model is effectively screened, while for intermediate models, such as F4.5 and F5.0, the first effect dominates, resulting in an overall weaker clustering than in GR.

Clustering Results (Redshift-Space Correlation Functions):

• ELGs (Monopole xi 0): The 25% differences from GR observed in the real-space CF are seen similarly in the monopole of the redshift-space CF. This suggests that the effect described above can indeed be measured and used in real observations.

• ELGs (Quadrupole xi 2): The behavior is complicated because the velocity bias is small so that tracer galaxies of different type and haloes of different mass have the same velocity field, which in f(R) gravity can be significantly enhanced.

• LRGs: The FoG effect is much stronger in redshift space due to the larger host-halo masses. This decreases the monopole between 1–10 Mpc.

Conclusion:

In summary, galaxy clustering is a promising avenue for testing gravity models. While the LRG results show complex, non-monotonic behavior that complicates constraints, ELG clustering offers a clearer path for constraining even weak f(R) models by identifying the correct redshift where their deviations are maximized. The study also highlights that "it is risky to fix the HOD parameters empirically by matching the predicted projected 2PCF with the observed one, and that a detailed study of how MG affects galaxy formation is essential if we wish to test the models using galaxy clustering."

The core challenges presented in this paper—distinguishing subtle deviations between General Relativity (GR) and Modified Gravity (MG) models using galaxy clustering and HODs—require AI systems that move beyond simple pattern recognition into complex, physically constrained inference.

Here are the specific improvements to be implemented in an AI system designed for cosmological data analysis:

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Improvement: Integrate a Variational Autoencoder (VAE) or a Generative Adversarial Network (GAN) constrained by the underlying physics of halo mergers and assembly bias. The latent space must be explicitly structured to map to key astrophysical parameters (alpha sat for satellite clustering, M cut for cutoff mass, sigma 8, etc.) rather than being purely statistical.

What the Improved AI System Can Do:

• Constrained Parameter Inference: Instead of merely minimizing a chi squared likelihood over observed HOD binned data (which is prone to local minima), the system will generate physically plausible distributions in the latent space, effectively regularizing the parameter fitting process.

• Predicting Residual Trends: The system can predict expected systematic residual trends when comparing an observed HOD to a theoretical model (e.g., predicting that MG models should systematically shift the satellite occupation curve rightward relative to GR, even if the magnitude of the shift is small).

• Handling Saturation Effects: The AI can be trained on synthetic data covering varying degrees of saturation (where F4.5 and F4.0 HODs are nearly identical) and quantify the minimum required observational precision (N / N GR) needed to resolve the differences between two nearly identical models, providing a rigorous measure of required survey depth/volume.