Modelling halo number counts with evolution mapping

Accurately modelling the abundance of dark matter haloes, described by the Halo Mass Function (HMF), is essential for understanding the large-scale structure of the Universe (LSS): the HMF is a key ingredient in any halo-based model of other LSS statistics, including the galaxy distribution, and serves as a standalone observable in studies of cluster cosmology.
Although the HMF is primarily determined by the halo peak height, it is known to have additional dependencies on the cosmological parameters, as well as a weak scaling with redshift. These effects, of order 10%, are referred to as the non-universality of the HMF. Capturing the non- universality is crucial to fully exploit current and upcoming LSS surveys. In this talk, I will present a new HMF model calibrated on a suite of high-resolution cosmological simulations. Our model is grounded in the Evolution Mapping framework, which helps in identifying the key parameters driving the non-universality. It achieves per cent-level accuracy across a broad range of halo masses and redshifts, for many halo mass definitions and over a wide range of cosmological parameters, providing an accurate tool to model the abundance of haloes in a great variety of contexts. We find that departures from universality are driven by the shape of the linear matter power spectrum at halo scales and, as predicted in the context of Evolution Mapping, the recent history of cosmic structure formation, whose memory is encoded in the abundance of haloes. I will also show how evolution mapping simplifies and reduces the cost of training emulators of LSS statistics, such as the matter power spectrum and, again, the HMF.