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We study the halo mass function in the presence of a kurtosis type of primordial non‐Gaussianity. The kurtosis corresponds to the trispectrum as defined in Fourier space. The primordial trispectrum is commonly characterized by two parameters, τ NL  and  g  NL . We focus on τ NL  which is an important parameter to test the physics of multifield inflation models. As applications of the derived non‐Gaussian mass function, we consider the effects on the abundance of void structure, on early star formation and on formation of the most massive objects at high redshift. We show that by comparing the effects of primordial non‐Gaussianity on cluster abundance with that on void abundance, we can distinguish between the skewness and the kurtosis types of primordial non‐Gaussianity. As for early star formation, we show that the kurtosis type of primordial non‐Gaussianity seems on the average not to affect the reionization history of the Universe. However, at high redshifts (up to  z ≃ 20) such non‐Gaussianity does somewhat affect the early stages of reionization.

Modification of the halo mass function by kurtosis associated with primordial non‐Gaussianity