We outline a simple approach to understanding the physical origin of bias in the distribution of galaxies relative to that of dark matter. The rst step is to specify how collapsed, virialized halos of dark matter trace the overall matter distribution.We de ne the quantity M to be the halo mass that has typically just collapsed by the present day. It can then be shown that on large scales, halos of mass M are unbiased tracers of the underlying matter distribution. Halos with masses greater than M are positively biased, while halos less massive than M are antibiased with respect to the dark matter. These conclusions are independent of the assumed shape of the power spectrum. The next step is to make a connection between halos and the luminous galaxies we observe. We appeal to the results of semi-analytic models of galaxy formation that are tuned to t the observed luminosity functions of local groups and clusters. Using these models, we are able to specify the luminosities and morphological types of the galaxies contained within a halo of given mass at the present day.We have also used a high-resolution N-body simulation of a cold dark matter (CDM) universe to study the bias relation in more detail. The di erences between the galaxy and dark matter distributions are quanti ed using a number of di erent clustering statistics, including the power spectrum, the two-point correlation function, the void probability function and the one-point probability density function. We arrive at the following general conclusions:1. A comparison of the galaxy and dark matter density elds shows that linear biasing is a good description on large scales for galaxies of all types and luminosities.2. The bias factor b depends on the shape and normalization of the power spectrum. The lower the normalization, the larger the bias. More bias is obtained for spectra with more power on large scales. For \realistic" models, b ranges from 1 to 2.5. 3. Galaxies of di erent luminosity or morphology have di erent bias factors. 4. The scale dependence of the bias factor is weak.

We study the quasilinear evolution of the one-point probability density functions (PDFs) of the smoothed density and velocity fields in a cosmological gravitating system beginning with Gaussian initial fluctuations. Our analytic results are based on the Zel'dovich approximation and laminar flow. A numerical analysis extends the results into the multistreaming regime using the smoothed fields of a CDM N-body simulation. We find that the PDF of velocity, both Lagrangian and Eulerian, remains Gaussian under the laminar Zel'dovich approximation, and it is almost indistinguishable from Gaussian in the simulations. The PDF of mass density deviates from a normal distribution early in the quasilinear regime and it develops a shape remarkably similar to a lognormal distribution with one parameter, the rms density fluctuation σ. Applying these results to currently available data we find that the PDFs of the velocity and density fields, as recovered by the P OT ENT procedure from observed velocities assuming Ω = 1, or as deduced from a redshift survey of IRAS galaxies assuming that galaxies trace mass, are consistent with Gaussian initial fluctuations.

The great advances in the network of cosmological tests show that the relativistic Big Bang theory is a good description of our expanding universe. But the properties of nearby galaxies that can be observed in greatest detail suggest a still better theory would more rapidly gather matter into galaxies and groups of galaxies. This happens in theoretical ideas now under discussion.In the standard cosmology [1] 4% of the mass of the universe is in the baryons of which stars and planets are made, 22% is nonbaryonic dark matter (DM), and the rest is Einstein's cosmological constant (or acts like it). Gravity has collected the dark matter in concentrations termed DM halos. In larger DM halos baryons were dense enough to have radiated away enough energy to collapse to galaxies and stars. The most massive halos, natural homes for the most luminous galaxies, preferentially form in regions of the highest local mass density.Less massive halos, natural homes for less luminous galaxies, appear in regions extending to lower local densities, in ridges of matter running between denser regions, forming a cosmic web [2] of filaments and sheets (as in Figs. 1 and 2 in [3]). This can be compared to the situation in our immediate extragalactic neighborhood illustrated in Figure 1. The Local Sheet at SGZ = 0 certainly looks like part of the cosmic web of the standard cosmology, but there are problems.Our selection of observations that seem to be pointing to an improved theory commences with the least crowded place in Figure 1, the Local Void, which contains far fewer galaxies than expected, while there is an unexpected presence of large galaxies on the outskirts of the Local Void. These problems would be eased if structure grew more rapidly than in the standard theory, more completely emptying the Local Void and piling up matter on its outskirts. In about half of the largest galaxies in Figure 1 the stars are largely confined

We present a new method for recovering the underlying velocity eld from an observed distribution of galaxies in redshift space. The method is based on a kinematic Zel'dovich relation between the velocity and density elds in redshift space. This relation is expressed in a di erential equation slightly modi ed from the usual Poisson equation, and which depends non-trivially on 0:6 =b. The linear equation can be readily solved by standard techniques of separation of variables by means of spherical harmonics. One can also include a term describing the \rocket e ect" discussed by Kaiser (1987). From this redshift space information alone, one can generate a prediction of the peculiar velocity eld for each harmonic (l; m) as a function of distance. We note that for the quadrupole and higher order moments, the equation is a boundary value problem with solutions dependent on both the interior and exterior mass distribution. However, for a shell at distance r, the dipole, as well as the monopole, of the velocity eld in the Local Group frame is fully determined by the interior mass distribution. This implies that the shear of the measured velocity eld, when t to a dipole distortion, should be aligned and consistent with the gravity eld inferred from the well determined local galaxy distribution. As a preliminary application we compute the velocity dipole of distant shells as predicted from the 1.2Jy IRAS survey compared to the measured velocity dipole on shells, as inferred from a recent POTENT analysis. The coherence between the two elds is good, yielding a best estimate of = 0:6 0:2.