LARGE-SCALE POWER SPECTRUM FROM PECULIAR VELOCITIES

The power spectrum (PS) of mass density fluctuations, in the range 0.0 5 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 gala xies, independent of ''biasing.'' It is computed from the density fiel d as recovered by POTENT with Gaussian smoothing of 12 h(-1) Mpc, with in a sphere of radius similar to 60 h(-1) Mpc about the Local Group. T he density is weighted inversely by the square of the errors. The PS i s corrected for the effects of smoothing, random errors, sparse sampli ng, and finite volume using mock catalogs that mimic in detail the Mar k III catalog and the dynamics of our cosmological neighborhood. The m ock 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 yiel ds 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 der ived from sky and redshift surveys show a similarity in shape and yiel d for beta = Omega(0.6)/b values in the range 0.77-1.21, with a typica l error of +/-0.1 per galaxy sample. A comparison of the mass PS at si milar to 100 h(-1) Mpc with the large-angle cosmic microwave backgroun d fluctuations by COBE provides constraints on cosmological parameters and on the slope of the initial PS (n). The ''standard'' cold dark ma tter model is marginally rejected at the similar to 2 sigma level, whi le each of the following modifications leads to a good fit: n less tha n or similar to 1, Omega(nu) similar to 0.3, or Omega less than or sim ilar to 1. Values of Omega as low as similar to 0.2 are ruled out with high confidence (independent of Lambda).