Large scale bias and the peak background split

Dark matter haloes are biased tracers of the underlying dark matter distribution. We use a simple model to provide a relation between the abundance of dark matter haloes and their spatial distribution on large scales. Our model shows that knowledge of the unconditional mass function alone is sufficient to provide an accurate estimate of the large-scale bias factor. We then use the mass function measured in numerical simulations of SCDM, OCDM and ΛCDM to compute this bias. Comparison with these simulations shows that this simple way of estimating the bias relation and its evolution is accurate for less massive haloes as well as massive ones. In particular, we show that haloes that are less/more massive than typical M* haloes at the time they form are more/less strongly clustered than is predicted by formulae based on the standard Press–Schechter mass function.