Halo assembly in cold and warm dark matter during the JWST frontier epoch

The JWST mission is in the process of probing the galaxy mass function at $z>10$, when conceivably any delay in halo assembly due to the presence of a dwarf galaxy-scale power spectrum cutoff may drastically suppress the number of galaxies relative to the cold dark matter (CDM) expectation. We employ N-body simulations of CDM and warm dark matter (WDM) to explore how the difference in halo collapse time between these models scales with $z=0$ descendant halo mass. We demonstrate that collapse begins first for the most massive haloes, and the delay in collapse time between CDM and WDM haloes correlates inversely with descendant mass. We thus infer that only present-day dwarf galaxies exhibit any difference in their assembly history between CDM and WDM at $z=10$, and therefore support previous studies that have found JWST is unlikely to determine whether our Universe is better described by the CDM cosmology or the WDM cosmology without favourable lensing studies.