Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA

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  • 5 February 2001
Abstract
We allow for nonlinear effects in the likelihood analysis of galaxy 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 a flat LCDM model (h=0.65, n=1, COBE) with only Om_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/Mpc 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 Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with sigma_8*Om_m^0.6 =0.49+-0.06 and 0.63+-0.08, in agreement with constraints from other data. The quoted 90% errors include cosmic variance. The improvement in the likelihood due to the nonlinear correction is very significant for MarkIII and moderately significant for SFI. When allowing deviations from LCDM, we find an indication for a wiggle in the power spectrum: an excess near k=0.05 and a deficiency at k=0.1 -- a "cold flow". This may be related to the wiggle seen in the power spectrum 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 and reduces a spatial gradient that was of concern in the purely linear analysis. The Principal Component Analysis (PCA) allows us to address spatial features of the data and to fine-tune the theoretical and error models. We address the potential for optimal data compression using PCA.

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