The pair-weighted relative velocity dispersion of galaxies provides a measure of the thermal energy of fluctuations of the observed galaxy distribution , but the measure is difficult to interpret and is very sensitive to the existence of rare , rich clusters of galaxies .
Several alternative statistical procedures have recently been suggested to relieve these problems .
We apply a variant of the object-weighted statistical method of Davis , Miller , & White ( 1997 ) to the Las Campanas Redshift Survey ( LCRS ) , which is the largest and deepest existing redshift survey that is nearly fully sampled .
The derived one-dimensional dispersion on scales \sim 1 { h ^ { -1 } { Mpc } } is quite low : \sigma _ { 1 } = 126 \pm 10 { km { s } ^ { -1 } } , with a modest decrease at larger scales .
The statistic is very stable ; the six independent slices of the LCRS all yield consistent results .
We apply the same statistical procedure to halos in numerical simulations of an open cosmological model and flat models with and without a cosmological constant .
In contrast to the LCRS , all the models show a dispersion which increases for scales > 1 { h ^ { -1 } { Mpc } } ; it is uncertain whether this is a numerical artifact or a real physical effect .
The standard cluster-normalized Cold Dark Matter model with \Omega _ { m } = 1 as well as a tilted variant with n = 0.8 yield dispersions substantially hotter than the LCRS value , while models with low matter density ( \Omega _ { m } = 0.3 ) are broadly consistent with the LCRS data .
Using a filtered cosmic energy equation , we measure \Omega _ { m } \approx 0.2 , with small-scale bias factors b = 1.0 – 1.5 for high-density models and b = 0.7 – 1.1 for low-density models .