The non-Gaussian halo mass function withfNL,gNLand τNL

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 f NL , 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 f NL model, we consider g NL Φ 3 -type non-Gaussianity and models where the 4-point amplitude τ NL 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.