Halo models of large scale structure

We review the formalism and applications of the halo-based description of non-linear gravitational clustering. In this approach, all mass is associated with virialized dark matter halos; models of the number and spatial distribution of the halos, and the distribution of dark matter within each halo, are used to provide estimates of how the statistical properties of large scale density and velocity fields evolve as a result of non-linear gravitational clustering. We first describe the model, and demonstrate its accuracy by comparing its predictions with exact results from numerical simulations of non-linear gravitational clustering. We then present several astrophysical applications of the halo model: these include models of the spatial distribution of galaxies, the non-linear velocity, momentum and pressure fields, descriptions of weak gravitational lensing, and estimates of secondary contributions to temperature fluctuations in the cosmic microwave background.