How well do we know the halo mass function?

Abstract The parameters governing the standard Λ 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 ΩM – 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 third WMAP data release, but the rate of this reduction is slowing. This is limited by uncertainty in the normalization σ8, 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 ΩM, and we comment briefly on optimal survey strategies for constraining dark matter and dark energy models using the HMF.