Mass Function Predictions Beyond LCDM

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. 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 $Λ$CDM cosmology and for a set of $w$CDM cosmologies. For the reference $Λ$CDM 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) $Λ$CDM mass function over a mass range of $6\cdot 10^{11}-3\cdot 10^{15}$ M$_{\odot}$ to an estimated accuracy of about 2%. The set of $w$CDM cosmologies is taken from the Coyote Universe simulation suite. The mass functions from this suite (which includes a $Λ$CDM cosmology and others with $w\simeq-1$) are described by the fitting formula for the reference $Λ$CDM 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.

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