How dark matter halos get their cusps

This talk derives dark-matter halo profiles from their assembly using a coarse-grained Boltzmann–Poisson treatment with a continuous subhalo population. A self-similar solution connects mass-growth rate to density slope, including gravitational scattering and capture. Initial collapse produces a three-halves cusp; hierarchical accretion and stable clustering favour the inner NFW slope; stalled growth approaches its outer slope. The framework ties these familiar profiles to successive dynamical stages rather than imposing them phenomenologically.