How well do we know the Halo Mass Function?
  The parameters governing the standard \Lambda Cold Dark Matter cosmological
model have been constrained with unprecedented accuracy by precise measurements
of the cosmic microwave background by the Wilkinson Microwave Anisotropy Probe
(WMAP) and Planck satellites. Each new data release has refined further our
knowledge of quantities -- such as the matter density parameter \Omega_M --
that are imprinted on the dark matter halo mass function (HMF), a powerful
probe of dark matter and dark energy models. In this letter we trace how
changes in the cosmological parameters over the last decade have influenced
uncertainty in our knowledge of the HMF. We show that this uncertainty has
reduced significantly since the 3rd WMAP data release, but the rate of this
reduction is slowing. This is limited by uncertainty in the normalisation
\sigma_8, whose influence is most pronounced at the high mass end of the mass
function. Interestingly, we find that the accuracy with which we can constrain
the HMF in terms of the cosmological parameters has now reached the point at
which it is comparable to the scatter in HMF fitting functions. This suggests
that the power of the HMF as a precision probe of dark matter and dark energy
hinges on more accurate determination of the theoretical HMF. Finally, we
assess prospects of using the HMF to differentiate between Cold and Warm Dark
Matter models based on ongoing improvements in measurements of \Omega_M, and we
comment briefly on optimal survey strategies for constraining dark matter and
dark energy models using the HMF.
