Cosmic Momentum Field and Mass Fluctuation Power Spectrum

We introduce the cosmic momentum field as a new measure of the large-scale peculiar velocity and matter fluctuation fields. The momentum field is defined as the peculiar velocity field traced and weighted by galaxies, and is equal to the velocity field in the linear regime. We show that the radial component of the momentum field can be considered as a scalar field with the power spectrum which is practically 1/3 of that of the total momentum field. We present a formula for the power spectrum directly calculable from the observed radial peculiar velocity data. The momentum power spectrum is measured for the MAT sample in the Mark III catalog of peculiar velocities of galaxies. Using the momentum power spectrum we find the amplitude of the matter power spectrum is 6400^{+2800}_{-1800} and 4500^{+2000}_{-1300} \Omega^{-1.2} (h^{-1} Mpc)^{-3} at the wavenumbers 0.049 and 0.074 h Mpc^{-1}, respectively, where \Omega is the density parameter. The 68% confidence limits include the cosmic variance. The measured momentum and density power spectra together indicate that the parameter \beta_O = \Omega^{0.6}/b_O = 0.51^{+0.13}_{-0.08} or \Omega = 0.33^{+0.15}_{-0.09} b_O^{5/3} where b_O is the bias factor for optical galaxies.