We allow for nonlinear e †ects in the likelihood analysis of galaxy peculiar velocities and obtain D35% lower values for the cosmological density parameter and for the amplitude of mass density ) m Ñuctuations This result is obtained under the assumption that the power spectrum in the linear p 8 ) m 0.6. regime is of the Ñat "CDM model (h \ 0.65, n \ 1, COBE normalized) with only as a free parameter. ) m Since the likelihood is driven by the nonlinear regime, we "" break ÏÏ the power spectrum at (h~1 k b D 0.2 Mpc)~1 and Ðt a power law at This allows for independent matching of the nonlinear behavior k [ k b . and an unbiased Ðt in the linear regime. The analysis assumes Gaussian Ñuctuations and errors and a linear relation between velocity and density. Tests using mock catalogs that properly simulate nonlinear e †ects demonstrate that this procedure results in a reduced bias and a better Ðt. We Ðnd for the Mark III and SFI data and 0.37^0.09, respectively, with and ) m \ 0.32^0.06 p 8 ) m 0.6 \ 0.49^0.06 0.63^0.08, in agreement with constraints from other data. The quoted 90% errors include distance errors and cosmic variance, for Ðxed values of the other parameters. The improvement in the likelihood due to the nonlinear correction is very signiÐcant for Mark III and moderately signiÐcant for SFI.When allowing deviations from "CDM, we Ðnd an indication for a wiggle in the power spectrum : an excess near k D 0.05 (h~1 Mpc)~1 and a deÐciency at k D 0.1 (h~1 Mpc)~1, or a "" cold Ñow.ÏÏ 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 s2 test applied to modes of a principal component analysis (PCA) shows that the nonlinear procedure improves the goodness of Ðt 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 Ðne-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.

We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be of the flat LCDM model (h=0.65, n=1) with only Om_m free. Since the likelihood is driven by the nonlinear regime, we "break" the power spectrum at k_b=0.2 h/Mpc and fit a two-parameter power-law at k>k_b. This allows for an unbiased fit in the linear regime. Tests using improved mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark III and SFI data Om_m=0.35+-0.09$ with sigma_8*Om_m^0.6=0.55+-0.10 (90% errors). When allowing deviations from \lcdm, we find an indication for a wiggle in the power spectrum in the form of an excess near k~0.05 and a deficiency at k~0.1 h/Mpc --- a "cold flow" which may be related to a feature indicated from redshift surveys and the second peak in the CMB anisotropy. A chi^2 test applied to principal modes demonstrates that the nonlinear procedure improves the goodness of fit. The Principal Component Analysis (PCA) helps identifying spatial features of the data and fine-tuning the theoretical and error models. We address the potential for optimal data compression using PCA.Comment: 15 pages, LaTex, in Mining the Sky, July 31 - August 4, 2000, Garching, German