Nonlinear Peculiar-Velocity Analysis and PCA

Abstract.

We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain $\sim$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 $\Lambda$CDM model (h = 0.65, n = 1) with only $\Omega_{\rm m}$ free. Since the likelihood is driven by the nonlinear regime, we “break” the power spectrum at $k_{\rm b}\sim 0.2 (h^{-1}{\rm Mpc})^{-1}$ 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 $\Omega_{\rm m} = 0.35\pm 0.09$ with $\sigma_8\Omega_{\rm m}^{0.6} = 0.55\pm 0.10$ (90% errors). When allowing deviations from $\Lambda$CDM, we find an indication for a wiggle in the power spectrum in the form of an excess near $k \sim 0.05$ and a deficiency at $k \sim 0.1 (h^{-1}{\rm Mpc})^{-1}$ - 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.