The DESI DR1 Peculiar Velocity Survey: growth rate measurements from galaxy and momentum correlation functions

TL;DR

This work presents a joint measurement of the growth rate of structure, quantified by $f\sigma_8$, from DESI DR1 by combining velocity and galaxy clustering statistics. Using a non-linear model based on 1-loop Eulerian perturbation theory, multiple correlation functions (momentum auto-correlation, galaxy monopole and quadrupole, and galaxy–momentum dipole) are simultaneously fitted to data and mocks to extract $f\sigma_8$ with a MCMC framework and mock-derived covariances. The analysis yields $f\sigma_8=0.391^{+0.080}_{-0.081}$ and, when combined with DR1 full-shape clustering, a growth-index constraint $\gamma_{\rm L}=0.580^{+0.110}_{-0.110}$, both consistent with General Relativity and Planck+$\Lambda$CDM predictions. A consensus DR1 result, combining three methodologies, is $f\sigma_8(z=0.07)=0.4497\pm0.0548$, demonstrating the potential of peculiar-velocity measurements to test gravity in the local universe, with significant gains anticipated from DESI DR2.

Abstract

Joint analysis of the local peculiar velocity and galaxy density fields offers a promising route to testing cosmological models of gravity. We present a measurement of the normalised growth rate of structure, $fσ_8$, from the two-point correlations of velocity and density tracers from the DESI DR1 Peculiar Velocity and Bright Galaxy Surveys, the largest catalogues of their kind assembled to date. We fit the two-point correlation measurements with non-linear correlation function models, constructed from density and momentum power spectra generated using 1-loop Eulerian perturbation theory, and validate our methodology using representative mock catalogues. We find $fσ_8 = 0.391^{+0.080}_{-0.081}$, consistent to within $1σ$ with accompanying analyses of the same datasets using power spectrum and maximum-likelihood fields methods. Combining these growth rate results from different methods including appropriate correlations, we find a consensus determination $fσ_8(z = 0.07) = 0.4497 \pm 0.0548$, consistent with predictions from \textit{Planck}$+Λ$CDM cosmology. Jointly fitting to this consensus low-redshift growth rate and the DESI DR1 full-shape clustering dataset, we measure gravitational growth index $γ_{\rm L} = 0.580^{+0.110}_{-0.110}$, consistent with the prediction of general relativity.

Figures (10)

• Figure 1: The $\psi_1$ correlation function for different velocity datasets tested in our analysis: the FP sample (black points), the TF sample (red points), the TF sample with a $z < 0.05$ cut (green points), and the combined sample (blue points). The solid line is the fiducial model. The original TF sample shows a high amplitude of correlation, leading us to apply a redshift cut $z < 0.05$ for the cosmological analysis.
• Figure 2: A visualisation of the geometry of two galaxies $A$ and $B$ in relation to an observer $O$. Vectors separating the observer from galaxies $A$ and $B$ are described by $\vec{r}_a$ and $\vec{r}_b$, respectively, while $\vec{r}$ is the vector separating $A$ and $B$. The three-dimensional velocity of the galaxies are represented by $\vec{v}_a$ and $\vec{v}_b$, while the measurable line of sight component of the velocity is given by $u_a$ and $u_b$. The cosines of the angles $\theta_a$, $\theta_b$, and $\theta_{ab}$ describe the relative locations of the observer and galaxy pair. The vector intersecting $\vec{r}$ that bisects the angle $\theta_{ab}$ is given by $\vec{d}$. The cosine of the angle between $\vec{r}$ and $\vec{d}$ is given by $\mu$. Adapted from a similar figure in Turner2025.
• Figure 3: The correlation matrix used in this analysis, generated from all 675 mocks and using the fitting range $24 - 120 \, h^{-1}$ Mpc for each statistic. For a bin width of $6 \, h^{-1}$ Mpc this corresponds to 16 bins per statistic, and hence a matrix with dimensions $80 \times 80$. We employ a colour bar such that bins with higher correlation are redder, and bins that exhibit more anti-correlation are bluer. Bins on the diagonal are perfectly correlated by construction. Bins that exhibit no correlation or anti-correlation are white.
• Figure 4: The five mock mean and data correlation functions that we consider in this analysis, and the best-fitting models for each. The light blue shaded region depicts the mock mean and $1\sigma$ errors as determined from all 675 mocks. The red points represents the measurements made from the DESI DR1 data, using BGS clustering data, FP velocity data, and the $z$-cut TF velocity data. The errors on these points are the same $1\sigma$ errors determined from the mocks. The black lines represent the best-fitting models generated using the parameters derived from the data, as shown in Figure \ref{['fig:data_corner']}, and the dashed blue lines represent the best-fitting models generated using the parameters derived from the mock mean, as shown in Figure \ref{['fig:mock_corner']}. We remind readers of the difference in the redshifts of the two datasets when interpreting this figure.
• Figure 5: The best-fitting values of $f\sigma_8$ for 300 of the AbacusSummit clustering and velocity mocks, plotted against the error in those values obtained from an MCMC analysis. The mock data includes both FP and TF velocity samples, and all five correlation function statistics were used to fit for the model parameters within a fitting range 24 - 120 $h^{-1}$ Mpc. The points are colour-coded by the minimum reduced $\chi^2$ value, as indicated by the colour bar in the upper left of the plot. The vertical dashed line represents the fiducial value of $f\sigma_8$ in the AbacusSummit mocks at the snapshot redshift $z = 0.20$. The dot-dashed line in red represents the ensemble error as a percentage, calculated as the standard deviation across the 300 best-fitting values of $f\sigma_8$. The dotted line in black represents the mean measurement error across the 300 mocks. The histograms on the top and right sides of the plot display the distribution of values of $f\sigma_8$ and $\sigma_{f\sigma_8}$, respectively.