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

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