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

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 Planck+ΛCDM 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.