Non-Markov Excursion Set Model of Dark Matter Halo Abundances

The excursion set model provides a convenient theoretical framework to derive dark matter halo abundances. This paper generalizes the model by introducing a more realistic merging and collapse process. A new parameter regulates the influence of the environment and thus the coherence (non-Markovianity) of the merging and the collapse of individual mass shells. The model mass function also includes the effects of an ellipsoidal collapse. Analytic approximations of the halo mass function are derived for scale-invariant power spectra with the slopes $n=0,-1,-2$. The $n=-2$ mass function can be compared with the results obtained from the `Hubble volume simulations. A significant detection of non-Markovian effects is found for an assumed accuracy of the simulated mass function of 10%.