Momentum power spectrum of SDSS galaxies by massE cosmic ruler: 2.1x improvement in measure of growth rate

Peculiar motion of galaxies probes the structure growth in the Universe. In this study we employ the galaxy stellar mass-binding energy (massE) relation with only two nuisance parameters to build the largest peculiar-velocity (PV) catalog to date, consisting of 229,890 ellipticals from the main galaxy sample (MGS) of the Sloan Digital Sky Survey (SDSS). We quantify the distribution of the massE-based distances in individual narrow redshift bins (dz=0.005), and then estimate the PV of each galaxy based on its offset from the Gaussian mean of the distribution. As demonstrated with the Uchuu-SDSS mock data, the derived PV and momentum power spectra are insensitive to accurate calibration of the massE relation itself, enabling measurements out to a redshift of 0.2, well beyond the current limit of z=0.1 using other galaxy scaling laws. We then measure the momentum power spectrum and demonstrate that it remains almost unchanged if varying significantly the redshift bin size within which the distance is measured, as well as the intercept and slope of the massE relation, respectively. By fitting the spectra using the perturbation theory model with four free parameters, fσ8 is constrained to fσ8 =0.459+0.068-0.069 over Δz=0.02-0.2, 0.416+0.074-0.076 over Δz=0.02-0.1 and 0.526+0.133-0.143 over Δz=0.1-0.2. The error of fσ8 is 2.1 times smaller than that by the redshift space distortion (RSD) of the same sample. A Fisher-matrix forecast illustrates that the constraint on fσ8 from the massE-based PV can potentially exceed that from the stage-IV RSD in late universe (z<0.5).