The Halo Mass Function from the Excursion Set Method. Iii. First Principle Derivation for Non-gaussian Theories

The high-mass tail of the dark matter halo mass function may be a sensitive probe of primordial nonGaussianities. In this paper, which is the third of a series of three, we perform a first-principle computation of the effect of primordial non-Gaussianity on the halo mass function using the excursion set method, where the evolution of the density perturbation with the smoothing scale is stochastic under the influence of a noise and the problem of computing the probability of halo formation is mapped into the so-called first-time passage problem in the presence of a barrier. The presence of non-Gaussianity causes the stochastic dynamics to be non-markovian and introduces “memory” effects. Using the formalism developed in the first paper of this series, and the diffusive barrier model developed in the second paper of this series, we compute the effect of the three-point correlator on the halo mass function and show that it is due entirely to memory effects. Our result reproduces recent N-body simulations with non-Gaussian initial conditions, without the introduction of any ad hoc parameter. Subject headings: cosmology:theory — dark matter:halos — large scale structure of the universe