Halo model description of the non-linear dark matter power spectrum at
  $k \gg 1$ Mpc$^{-1}$
  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 proper modeling 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.
