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We perform a series of high‐resolution  N ‐body simulations of cosmological structure formation starting from Gaussian and non‐Gaussian initial conditions. We adopt the best‐fitting cosmological parameters from the third‐ and fifth‐year data releases of the  Wilkinson Microwave Anisotropy Probe,  and we consider non‐Gaussianity of the local type parametrized by eight different values of the non‐linearity parameter  f  NL . Building upon previous work based on the Gaussian case, we show that, when expressed in terms of suitable variables, the mass function of friends‐of‐friends haloes is approximately universal (i.e. independent of redshift, cosmology and matter transfer function) to good precision (nearly 10 per cent) also in non‐Gaussian scenarios. We provide fitting formulae for the high‐mass end  ( M  &gt; 10 13   h  −1  M ⊙ )  of the universal mass function in terms of  f  NL , and we also present a non‐universal fit in terms of both  f  NL  and  z  to be used for applications requiring higher accuracy. For Gaussian initial conditions, we extend our fit to a wider range of halo masses  ( M  &gt; 2.4 × 10 10   h  −1  M ⊙ )  and we also provide a consistent fit of the linear halo bias. We show that, for realistic values of  f  NL , the matter power spectrum in non‐Gaussian cosmologies departs from the Gaussian 1 by up to 2 per cent on the scales where the baryonic‐oscillation features are imprinted on the two‐point statistics. Finally, using both the halo power spectrum and the halo‐matter cross spectrum, we confirm the strong  k ‐dependence of the halo bias on large scales  ( k  &lt; 0.05  h  Mpc −1 )  which was already detected in previous studies. However, we find that commonly used parametrizations based on the peak‐background split do not provide an accurate description of our simulations which present extra dependencies on the wavenumber, the non‐linearity parameter and, possibly, the clustering strength. We provide an accurate fit of the simulation data that can be used as a benchmark for future determinations of  f  NL  with galaxy surveys.

Halo mass function and scale‐dependent bias from N ‐body simulations with non‐Gaussian initial conditions