Large-Scale Mass Power Spectrum from Peculiar Velocities

The power spectrum of mass density fluctuations is estimated from the Mark III and the SFI catalogs of peculiar velocities by applying a maximum likelihood analysis, using parametric models for the power spectrum and for the errors. Generalized CDM models with and without COBE normalization are used. The applications to the two different data sets give consistent results. The general result is a relatively high amplitude of the power spectrum, eg, at k=0.1 h/Mpc we find P(k) \Omega^{1.2} = (4.5+/-2.0)X10^3 (Mpc/h)^3, corresponding to \sigma_8 \Omega^{0.6} = 0.85+/-0.2. Model-dependent constraints on combinations of cosmological parameters are obtained for families of COBE-normalized CDM models. These can roughly be approximated by \Omega h_{60}^\mu n^\nu = 0.6+/-0.2, where \mu=1.3 and \nu=3.7, 2.0 for flat \Lambda CDM models with and without tensor fluctuations respectively. For open CDM, without tensor fluctuations, the powers are \mu=0.9 and \nu=1.4. The quoted error-bars reflect the 90% formal likelihood uncertainty for each model and the variance among different models and between catalogs. This is a brief review of a collaborative project (for more details, see Zaroubi et al 1997, Freudling et al 1998). Preliminary constraints in the \Omega-\Lambda plane are presented as well.