Large-scale power spectrum from peculiar velocities

The power spectrum (PS) of mass density fluctuations, in the range 0.05 h Mpc(-1) less than or equal to k less than or equal to 0.2 h Mpc(-1), is derived from the Mark III catalog of peculiar velocities of galaxies, independent of ''biasing.'' It is computed from the density field as recovered by POTENT with Gaussian smoothing of 12 h(-1) Mpc, within a sphere of radius similar to 60 h(-1) Mpc about the Local Group. The density is weighted inversely by the square of the errors. The PS is corrected for the effects of smoothing, random errors, sparse sampling, and finite volume using mock catalogs that mimic in detail the Mark III catalog and the dynamics of our cosmological neighborhood. The mock catalogs are also used for error analysis. The PS at k = 0.1 h Mpc(-1) (for example) is (4.6 +/- 1.4) x 10(3) Omega(-1.2) (h(-1) Mpc)(3), with a local logarithmic slope of -1.45 +/- 0.5. An integration yields sigma(8) Omega(0.6) similar or equal to 0.7-0.8, depending on where the PS peak is. Direct comparisons of the mass PS with the galaxy derived from sky and redshift surveys show a similarity in shape and yield for beta = Omega(0.6)/b values in the range 0.77-1.21, with a typical error of +/-0.1 per galaxy sample. A comparison of the mass PS at similar to 100 h(-1) Mpc with the large-angle cosmic microwave background fluctuations by COBE provides constraints on cosmological parameters and on the slope of the initial PS (n). The ''standard'' cold dark matter model is marginally rejected at the similar to 2 sigma level, while each of the following modifications leads to a good fit: n less than or similar to 1, Omega(nu) similar to 0.3, or Omega less than or similar to 1. Values of Omega as low as similar to 0.2 are ruled out with high confidence (independent of Lambda).