Mass Function Predictions Beyond ΛCDM

The statistics of dark matter halos is an essential component of precision cosmology. The mass distribution of halos, as specified by the halo mass function, is a key input for several cosmological probes. The sizes of N-body simulations are now such that, for the most part, results need no longer be statistics-limited, but are still subject to various systematic uncertainties. Discrepancies in the results of simulation campaigns for the halo mass function remain in excess of statistical uncertainties and of roughly the same size as the error limits set by near-future observations; we investigate and discuss some of the reasons for these differences. Quantifying error sources and compensating for them as appropriate, we carry out a high-statistics study of dark matter halos from 67 N-body simulations to investigate the mass function and its evolution for a reference ΛCDM cosmology and for a set of wCDM cosmologies. For the reference ΛCDM cosmology (close to WMAP5), we quantify the breaking of universality in the form of the mass function as a function of redshift, finding an evolution of as much as 10% away from the universal form between redshifts z = 0 and z = 2. For cosmologies very close to this reference we provide a fitting formula to our results for the (evolving) ΛCDM mass function over a mass range of 6 × 10¹¹-3 × 10¹⁵ M _sun to an estimated accuracy of about 2%. The set of wCDM cosmologies is taken from the Coyote Universe simulation suite. The mass functions from this suite (which includes a ΛCDM cosmology and others with w ~= -1) are described by the fitting formula for the reference ΛCDM case at an accuracy level of 10%, but with clear systematic deviations. We argue that, as a consequence, fitting formulae based on a universal form for the mass function may have limited utility in high-precision cosmological applications.