  The halo model formalism is widely adopted in cosmological studies for
predicting the growth of large-scale structure in the Universe. However, to
date there have been relatively few direct comparisons of the halo model with
more accurate (but much more computationally expensive) cosmological
simulations. We test the accuracy of the halo model in reproducing the
non-linear matter power spectrum, P(k), when the main inputs of the halo model
(specifically the matter density profiles, halo mass function, and linear bias)
are taken directly from the BAHAMAS simulations and we assess how well the halo
model reproduces P(k) from the same simulations. We show that the halo model
generally reproduces P(k) in the deep non-linear regime (1-halo) to typically a
few percent accuracy, but struggles to reproduce (approx. 15% error) P(k) at
intermediate scales of 0.1 < k [h/ Mpc] < 3 at z=0, marking the transition
between the 1-halo and 2-halo terms. We show that the magnitude of this error
is a strong function of the halo mass definition (through its effects on radial
extent of haloes) and of redshift. Furthermore, we test the accuracy of the
halo model in recovering the relative impact of baryons on P(k). We show that
the systematic errors in recovering the absolute P(k) largely cancel when
considering the relative impact of baryons. This suggests that the halo model
can make precise predictions for the baryonic suppression, offering a fast and
accurate way to adjust collisionless matter power spectra for the presence of
baryons and associated processes.
