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Large-scale peculiar velocities through the galaxy luminosity function at z ~ 0.1

Peculiar motion introduces systematic variations in the observed luminosity distribution of galaxies. This allows one to constrain the cosmic peculiar velocity field from large galaxy redshift surveys. Using around half a million galaxies from the SDSS Data Release 7 at z ~ 0.1, we demonstrate the applicability of this approach to large datasets and obtain bounds on peculiar velocity moments and $σ_{8}$, the amplitude of the linear matter power spectrum. Our results are in good agreement with the $Λ$CDM model and consistent with the previously reported ~ 1% zero-point tilt in the SDSS photometry. Finally, we discuss the prospects of constraining the growth rate of density perturbations by reconstructing the full linear velocity field from the observed galaxy clustering in redshift space.