Emulating galaxy and peculiar velocity clustering on non-linear scales

TL;DR

This work tackles extracting cosmological information from non-linear galaxy clustering and peculiar-velocity fields by cross-correlating galaxies and velocities on non-linear scales. It deploys AbacusSummit N-body simulations together with a halo occupation distribution to train multi-scale Gaussian process emulators that predict redshift-space clustering multipoles for five observables. The results show that combining galaxy and velocity clustering tightens constraints on cosmological parameters, notably $σ_8$ and $w_0$, achieving a $3.8\%$ precision on $fσ_8$ in realistic mocks, though some biases appear in HOD parameters and gains depend on velocity measurement quality. The study highlights the potential of velocity tracers to enhance growth-rate measurements while underscoring the need to control velocity uncertainties and observational systematics on small scales for robust, unbiased cosmology.

Abstract

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.

Figures (10)

• Figure 1: Comparison between fixed and varying LoS estimators using of the 25 Planck2018 boxes with the median HOD. The solid lines show the mean clustering of the 25 boxes computed using Eqs \ref{['eq:LS_gg']} and \ref{['eq:LS_vv_vg']} with a full-sky spherical footprint and a redshift range of $z \in [0 ; 0.1]$. The shaded area are the corresponding standard deviation of the realisations. The dashed black lines show the mean of the flat-sky approximation clustering.
• Figure 2: Correlation matrix computed from 1400 small boxes realisations of the Planck2018 cosmology, using the median HOD. The different panels show the auto and cross correlation between the TPCF multipoles of $\xi_{gg}$ , $\xi_{vv}$ and $\xi_{gv}$. Each of the subplot axis correspond to the scale $s$ with a logarithmic binning going from $0.3~h^{-1}\mathrm{Mpc}$ to $60~h^{-1}\mathrm{Mpc}$.
• Figure 3: Comparison between the noisy and the noise-free measurements for peculiar velocity clustering using our set of 25 realistic mocks. The average of the 25 "true" clustering is shown in orange and our estimator is shown in blue. The shaded area is the standard deviation of the 25 mocks.
• Figure 4: Median Absolute Error (MAE) evaluated of the complete test set. The blue and orange solid lines in the top (middle) panel show the performance of the $\xi^{gg}_0$ and $\xi^{gg}_2$ ($\xi^{vv}_0$ and $\xi^{vv}_2$) models. The turquoise solid line in the bottom panel show the performance for $\xi^{vg}_1$. The shaded area estimate the expected accuracy on the test set as the median of $| \sigma/\xi^{\rm test} |$.
• Figure 5: Residuals $\Delta \xi \cdot L^{-1}$ with $L^{-1}$ the Cholesky decomposition of the inverse of the total covariance $C_{\rm tot} = C_{\rm cosmic} + C_{\rm emu}$. The blue and orange solid lines in the top panel show the performance of the $\xi^{gg}_0$ and $\xi^{gg}_2$ models. The same colours are used for $\xi^{vv}_0$ and $\xi^{vv}_2$ in the middle panel. The turquoise lines show the performance for $\xi^{vg}_1$ in the bottom panel. The grey shaded areas are the one and two sigma deviations.