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Accurate knowledge of the non‐linear dark matter power spectrum is important for understanding the large‐scale structure of the Universe, the statistics of dark matter haloes and their evolution, and cosmological gravitational lensing. We analytically model the dark matter power spectrum and its cross‐power spectrum with dark matter haloes. Our model extends the halo model formalism, including realistic substructure population within individual dark matter haloes and the scatter of the concentration parameter at fixed halo mass. We consider three prescriptions for the mass–concentration relation and two for the substructure distribution in dark matter haloes. We show that this extension of the halo model mainly increases the predicted power on the small scales and is crucial for properly modelling the cosmological weak‐lensing signal due to low‐mass haloes. Our extended formalism shows how the halo model approach can be improved in accuracy as one increases the number of ingredients that are calibrated from  N ‐body simulations.

Halo model description of the non‐linear dark matter power spectrum at k ≫ 1 Mpc −1