4.1. Measured Peculiar Velocities

These methods use data that include both redshifts and redshift-independent distances to galaxies via POTENT-like reconstructions of the underlying velocity and mass-density fields [34], independently of whole-sky redshift surveys. Combined with the assumption of Gaussian initial fluctuations, these methods provide lower bounds on _m in various ways [35], such as (a) using the fact that diverging flows in voids cannot be large when _m is low because the voids cannot be more empty than empty [36], (b) using the skewness of . v as induced by _m-dependent nonlinear gravity [37], and (c) appealing to the mass-density initial probability distribution function via a Zel'dovich ``time machine'' [38].

New developments: The Mark III catalog of Tully-Fisher and D_n - peculiar velocities with more than 3000 galaxies has been completed [39], and several new samples are coming up soon. New, more accurate distance indicators are being developed and implemented to larger samples. Most promising are the methods based on surface-brightness fluctuations for nearby galaxies, and supernovae type Ia for large-scale coverage ([40] for a review). The understanding of the systematic biases in the data and the analysis is improving, and new methods for correcting them are being developed.

Pro: These methods allow direct dynamical measures of _m independent of galaxy density biasing.

Con: The measurement of redshift-independent distances involves large errors that grow in proportion to distance, and the analysis is therefore limited to the relatively local cosmological volume, out to ~ 100 h^-1Mpc in the best cases. The associated cosmic scatter is inevitably large. Some of the distance indicators may be subject to systematic environmental effects that are hard to identify. These methods ignore possible velocity biasing. The methods assume potential flow and Gaussian initial conditions. These are valid hypotheses for the standard scenarios of structure formations, but they might be invalid in more esoteric models, such as those based on topological defects as seeds for structure formation.

Current Results: From Mark III peculiar velocities using several methods: _m > 0.3 at more than 95% confidence (reviews: [35]). From the extracted mass power spectrum under the general CDM family of models [41]: _{8 m}^0.6 = 0.8 ± 0.2.