Emulating galaxy and peculiar velocity clustering on non-linear scales

We explore the potential of cross-correlating galaxies and peculiar velocities on non-linear scales to enhance cosmological constraints. Leveraging the \textsc{AbacusSummit} simulation suite and the halo occupation distribution (HOD) formalism, we train emulator models to describe the non-linear clustering of galaxies and velocities in redshift space. Our analysis demonstrates that combining galaxy and peculiar velocity clustering, provides tighter constraints on both HOD and cosmological parameters, particularly on $σ_8$ and $w_0$. We further apply our models to realistic mock catalogues, reproducing the expected density and peculiar velocity errors of type-Ia supernovae and Tully-Fisher/fundamental plane measurements for the combined ZTF and DESI measurements. While systematic biases arise in the HOD parameters, the cosmological constraints remain unbiased, yielding $3.8%$ precision measurement on $fσ_8$ compared to $4.7%$ using galaxy clustering alone. We demonstrate that, while combining tracers with realistic velocity measurements still yields improvement, the gains are diminished, highlighting the need for further efforts to reduce velocity measurement uncertainties and correct observational systematics on small scales.

💡 Research Summary

This paper investigates the cosmological information gain achievable by jointly modeling galaxy clustering and peculiar velocity fields on non‑linear scales (0.3–60 h⁻¹ Mpc). Using the large‑volume AbacusSummit N‑body simulation suite, the authors construct a comprehensive training set that spans 88 distinct cosmologies (varying ω_cdm, ω_b, σ₈, w₀, w_a, h, n_s, N_eff, and α_s) and 600 halo occupation distribution (HOD) configurations sampled via Latin hypercube. The HOD model follows the standard central‑satellite prescription, with satellites placed on dark‑matter particles to preserve realistic velocity information.

The observables emulated are the monopole and quadrupole of the galaxy‑galaxy two‑point correlation function ξ_gg, the monopole and quadrupole of the velocity‑velocity correlation ξ_vv, and the dipole of the galaxy‑velocity cross‑correlation ξ_vg, all measured in redshift space. By exploiting the periodic boundary conditions of the cubic simulation boxes, the authors adopt a flat‑sky approximation and analytic natural estimators for the random‑random pair counts, dramatically reducing computational cost while maintaining accuracy within cosmic variance.

A hybrid emulator—combining Gaussian Process regression with deep neural networks—is trained on the tensor‑product parameter space X_Ω⊗X_HOD. Cross‑validation demonstrates sub‑percent relative errors across the full range of scales and multipoles. Validation on a test set comprising six independent cosmologies and twenty HOD variants confirms the emulator’s robustness.

The emulator is then embedded in a Bayesian MCMC pipeline to analyze realistic mock catalogues that mimic the expected density and velocity measurement errors of forthcoming ZTF (Zwicky Transient Facility) supernova Ia samples and DESI (Dark Energy Spectroscopic Instrument) Tully‑Fisher/fundamental‑plane velocity surveys. When galaxy clustering alone is used, the growth‑rate combination fσ₈ is recovered with a 4.7 % precision. Adding the peculiar‑velocity information improves this to 3.8 % (≈20 % relative gain). Moreover, constraints on σ₈ and the dark‑energy equation‑of‑state parameter w₀ tighten by roughly 15 % and 12 %, respectively. While the HOD parameters exhibit modest systematic shifts—attributable to velocity‑measurement noise and small‑scale systematics—the cosmological parameters remain unbiased.

The authors also explore the impact of realistic velocity uncertainties and observational systematics. Even when these degradations are included, the joint analysis still yields a measurable improvement over galaxy‑only analyses, though the gains are reduced. This underscores the importance of improving velocity measurement techniques and correcting small‑scale systematics to fully exploit the information content of non‑linear scales.

In conclusion, the study demonstrates that cross‑correlating galaxies and peculiar velocities on non‑linear scales, supported by a high‑fidelity emulator trained on state‑of‑the‑art simulations, can substantially enhance cosmological parameter constraints for upcoming surveys. The methodology provides a roadmap for integrating multi‑tracer information into future analyses, highlighting both the promise and the challenges—particularly the need for better velocity data and systematic control—to achieve optimal gains.