Large‐Scale Power Spectrum from Peculiar Velocities

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Abstract
The power spectrum (PS) of mass density fluctuations, in the range 0.05 h Mpc-1 ≤ k ≤ 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 ~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) × 103 Ω-1.2 (h-1 Mpc)3, with a local logarithmic slope of -1.45 ± 0.5. An integration yields σ8Ω0.6 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 β ≡ Ω0.6/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 ~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 ~2 σ level, while each of the following modifications leads to a good fit: n 1, Ων ~ 0.3, or Ω 1. Values of Ω as low as ~0.2 are ruled out with high confidence (independent of Λ).

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