The James Webb Space Telescope (JWST) has found surprisingly massive galaxies and bright active galactic nuclei (AGN) very early in the Universe. This paper asks a basic but powerful question: given standard cosmology, are there enough dark-matter halos to host those objects? The authors build a clear, number-based test that links the cosmic supply of halos to the observed populations of galaxies and AGN.

The researchers present a unified framework that starts from the linear matter power spectrum — a description of how small density differences were distributed across scales in the early Universe — and carries it through to quantities that cosmologists use to count halos. These steps include the mass variance and a ‘‘peak height’’ that measures how rare a halo of given mass is, then the halo mass function (HMF), which gives the number of halos per mass and redshift. They use the Sheth–Tormen (ST) halo mass function as their baseline, compare it to a Bolshoi/Klypin-calibrated modification called KST, and also refer to the older Press–Schechter (PS) model as a simple reference.

With that cosmological supply in hand, they apply three complementary tests. First is a baryonic-reservoir test: the cosmic baryon fraction limits how much stellar mass a halo can produce, so the HMF must provide enough halos of the right mass to explain the observed massive galaxies. Second is an AGN host-abundance test: the halo population is combined with a minimum host mass, a black-hole occupation fraction (what fraction of halos actually host a black hole), and an AGN duty cycle (the fraction of time a black hole shines as an AGN) to predict how many active systems should be seen. Third is a rest-frame ultraviolet (UV) luminosity-function test: a controlled mapping from halo mass to UV light yields a predicted UV galaxy population to compare with JWST counts.