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

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 $f\sigma_8 = 0.483_{-0.043}^{+0.080}(\mathrm{stat}) \pm 0.018(\mathrm{sys})$, consistent within $1\sigma$ with the power spectrum and correlation function analysis using the same dataset. Combining all three measurements with appropriate correlations, the consensus measurement is $f\sigma_8 (z_{\mathrm{eff}}=0.07) = 0.450\pm0.055$, consistent with Planck $+\Lambda$CDM cosmology $(f\sigma_8 = 0.449 \pm 0.008)$. Combining with the high redshift growth rate of structure measurements from DESI ShapeFit, the constraint on the growth index is $\gamma = 0.58\pm0.11$, consistent with GR.