© CAMBRIDGE UNIVERSITY PRESS 1999

1.4.2 Large-scale Measurements

₀ has been measured with some precision on a scale of about ~ 50 h^-1 Mpc, using the data on peculiar velocities of galaxies, and on a somewhat larger scale using redshift surveys based on the IRAS galaxy catalog. Since the results of all such measurements to date have been reviewed in detail (see Ch. 7; also see Dekel 1994, Strauss & Willick 1995), only brief comments are provided here. The ``POTENT'' analysis tries to recover the scalar velocity potential from the galaxy peculiar velocities. It looks reliable, since it reproduces the observed large scale distribution of galaxies - that is, many galaxies are found where the converging velocities indicate that there is a lot of matter, and there are voids in the galaxy distribution where the diverging velocities indicate that the density is lower than average. The comparison of the IRAS redshift surveys with POTENT and related analyses typically give fairly large values for the parameter _{I 0}^0.6 / b_I (where b_I is the biasing parameter for IRAS galaxies), corresponding to 0.3 ₀ 3 (for an assumed b_I = 1.15). It is not clear whether it will be possible to reduce the spread in these values significantly in the near future - probably both additional data and a better understanding of systematic and statistical effects will be required.

A particularly simple way to deduce a lower limit on ₀ from the POTENT peculiar velocity data was proposed by Dekel & Rees (1994), based on the fact that high-velocity outflows from voids are not expected in low- models. Data on just one void indicates that ₀ 0.3 at the 97% C.L. This argument is independent of assumptions about or galaxy formation, but of course it does depend on the success of POTENT in recovering the peculiar velocities of galaxies.

However, for the particular cosmological models that are at the focus of this review - CHDM and CDM - stronger constraints are available. This is because these models, in common with almost all CDM variants, assume that the probability distribution function (PDF) of the primordial fluctuations was Gaussian (the assumption of Gaussianity is also supported by observations, cf. Section 7.4.5). The PDF deduced by POTENT from observed velocities (i.e., the PDF of the mass, if the POTENT reconstruction is reliable) is far from Gaussian today, with a long positive-fluctuation tail and a sharp drop for negative / (e.g., respecting the requirement that 0). It agrees with a Gaussian initial PDF if and only if is about unity: ₀ 0.3 is ruled out at a high sigma level (Section 7.5.2; i.e., Nusser & Dekel 1993; Bernardeau et al. 1995).