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Primordial non-Gaussianity has emerged as one of the most promising probes ofthe inflationary epoch. While the cosmic microwave background and large-scalehalo bias currently provide the most stringent constraints on the non-Gaussianparameter fNL, the abundance of dark matter halos is a complementary probewhich may allow tests of Gaussianity which are independent of the precise formof non-Gaussian initial conditions. We study the halo mass function in N-bodysimulations with a range of non-Gaussian initial conditions. In addition to theusual fNL model, we consider gNL Phi^3-type non-Gaussianity and models wherethe 4-point amplitude tauNL is an independent parameter. We introduce a newanalytic form for the halo mass function in the presence of primordialnon-Gaussianity, the "log-Edgeworth" mass function, and find good agreementwith the N-body simulations. The log-Edgeworth mass function introduces no freeparameters and can be constructed from first principles for any model ofprimordial non-Gaussianity.

The Non-Gaussian Halo Mass Function with fNL, gNL and tauNL