The DESI DR1 Peculiar Velocity Survey: growth rate measurements from the maximum likelihood fields method

TL;DR

This paper presents a joint DESI DR1 analysis of peculiar velocity and galaxy-density fields using the maximum likelihood fields method to constrain the growth rate of structure, quantified by $f\sigma_8$. It introduces a fast, analytic covariance framework and implements computational accelerations with JAX to handle large DESI datasets, validating the method on 675 AbacusSummit mocks. The authors report a DESI DR1 consensus constraint $f\sigma_8(z_{eff}=0.07)=0.450\pm0.055$, consistent with Planck $\Lambda$CDM and GR, and, when combined with higher-redshift ShapeFit measurements, a growth index $\gamma=0.58\pm0.11$, in agreement with GR. The work demonstrates unbiased recovery on mocks, tightens low-redshift growth-rate constraints relative to prior PV analyses, and highlights systematic uncertainties associated with the nonlinear velocity damping parameter, proposing paths for future improvements through data compression and free-parameter treatments.

Abstract

We present the constraint on the growth rate of structure from the combination of DESI DR1 BGS sample, Fundamental Plane, and Tully-Fisher peculiar velocity catalogues using the maximum likelihood fields method. The combined catalogue contains 415,523 galaxy redshifts and 76,616 peculiar velocity measurements. To handle the large amount of data in the DESI DR1 peculiar velocity catalogue, we significantly improve the computational efficiency by rewriting the algorithm with JAX. After removing outliers and Tully-Fisher galaxies that are affected by systematics, we find $fσ_8 = 0.483_{-0.043}^{+0.080}(\mathrm{stat}) \pm 0.018(\mathrm{sys})$, consistent within $1σ$ with the power spectrum and correlation function analysis using the same dataset. Combining all three measurements with appropriate correlations, the consensus measurement is $fσ_8 (z_{\mathrm{eff}}=0.07) = 0.450\pm0.055$, consistent with Planck $+Λ$CDM cosmology $(fσ_8 = 0.449 \pm 0.008)$. Combining with the high redshift growth rate of structure measurements from DESI ShapeFit, the constraint on the growth index is $γ= 0.58\pm0.11$, consistent with GR.

Figures (13)

• Figure 1: The distribution of Fundamental Plane (FP; circle, left) and Tully-Fisher (TF; diamond, right) galaxies in the DESI DR1 peculiar velocity catalogue. Their colours indicate the galaxies' redshifts. The DESI DR1 peculiar velocity catalogue mainly covers the northern hemisphere.
• Figure 2: The redshift distribution of galaxies in the DESI DR1 Fundamental Plane and Tully-Fisher catalogue. The histogram shows the number of galaxies in each redshift bin, and the dashed line shows the number density of galaxies per unit volume in each redshift bin. The distribution of galaxies in the Fundamental Plane catalogue skews towards higher redshift, while the galaxies in the Tully-Fisher catalogue peak at low redshift. However, the number density of galaxies from both catalogues peaks at low redshift.
• Figure 3: Distribution of the log-distance ratios $\eta$ in the Fundamental Plane, Tully-Fisher, and the combined catalogues. The plot on the right is the normalised probability density. The Fundamental Plane catalogue skews towards a more negative log-distance ratio, while the Tully-Fisher catalogue skews towards a more positive log-distance ratio.
• Figure 4: The damping on the power spectrum introduced by the gridding kernel and the RSD damping on the velocity field $D_u$. The gridding kernel and the RSD damping are degenerate. The gridding kernel with a $20h^{-1}\mathrm{Mpc}$ grid size is similar to applying the RSD damping with $\sigma_u = 10h^{-1} \mathrm{Mpc}$. Similarly, the gridding kernel with a $30h^{-1}\mathrm{Mpc}$ grid size is similar to applying the RSD damping with $\sigma_u = 15h^{-1} \mathrm{Mpc}$.
• Figure 5: The constraints on $f\sigma_8$ from 479 Tully-Fisher mocks with $\sigma_u = 10h^{-1} \mathrm{Mpc}$ and grid size of $20h^{-1} \mathrm{Mpc}$. The colour indicates the reduced chi-squared of each mock. The mock mean is consistent with the fiducial $f\sigma_8$ indicated by the blue dashed line.