The abundance and clustering of dark haloes in the standard ΛCDM cosmogony

Much evidence suggests that we live in a flat cold dark matter universe with a cosmological constant. Accurate analytic formulae are now available for many properties of the dark halo population in such a Universe. Assuming current ‘concordance’ values for the cosmological parameters, we plot halo abundance against redshift as a function of halo mass, halo temperature, the fraction of cosmic matter in haloes, halo clustering strength, and the clustering strength of the z = 0 descendants of high‐redshift haloes. These plots are useful for understanding how nonlinear structure grows in the model. They demonstrate a number of properties that may seem surprising, for example: 10 9 M ⊙ haloes are as abundant at z = 20 as L * galaxies are today; 10 6 K haloes are equally abundant at z = 8 and at z = 0; 10 per cent of all matter is currently in haloes hotter than 1 keV, while more than half is in haloes too cool to trap photo‐ionized gas; 1 per cent of all matter at z = 15 is in haloes hot enough to ionize hydrogen; haloes of given mass or temperature are more clustered at higher redshift; haloes with the abundance of present‐day L * galaxies are equally clustered at all z < 20 ; the metals produced by star‐formation at z > 10 are more clustered at z = 0 than are L * galaxies.