Cosmological density and power spectrum from peculiar velocities: Nonlinear corrections and principal component analysis

We allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities and obtain ∼ 35% lower values for the cosmological density parameter Ω_m and for the amplitude of mass density fluctuations σ₈Ω^0.6_m. This result is obtained under the assumption that the power spectrum in the linear regime is of the flat ACDM model (h = 0.65, n = 1, COBE normalized) with only Ω_m as a free parameter. Since the likelihood is driven by the nonlinear regime, we "break" the power spectrum at k_b ∼ 0.2 (h^-1 Mpc)^-1 and fit a power law at k > k_b. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors and a linear relation between velocity and density. Tests using mock catalogs that properly simulate nonlinear effects demonstrate that this procedure results in a reduced bias and a better fit. We find for the Mark III and SFI data Ω_m = 0.32 ± 0.06 and 0.37 ± 0.09, respectively, with σ₈ Ω^0.6_m = 0.49 ± 0.06 and 0.63 ± 0.08, in agreement with constraints from other data. The quoted 90% errors include distance errors and cosmic variance, for fixed values of the other parameters. The improvement in the likelihood due to the nonlinear correction is very significant for Mark III and moderately significant for SFI. When allowing deviations from ACDM, we find an indication for a wiggle in the power spectrum: an excess near k ∼ 0.05 (h^-1 Mpc)^-1 and a deficiency at k ∼ 0.1 (h^-1 Mpc)^-1, or a "cold flow." This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the cosmic microwave background (CMB) anisotropy. A X² test applied to modes of a principal component analysis (PCA) shows that the nonlinear procedure improves the goodness of fit and reduces a spatial gradient that was of concern in the purely linear analysis. The PCA allows us to address spatial features of the data and to evaluate and fine-tune the theoretical and error models. It demonstrates in particular that the models used are appropriate for the cosmological parameter estimation performed. We address the potential for optimal data compression using PCA.