New Halo Accretion Framework Bridges Primordial Fluctuations to Galaxy Growth Across Cosmic Time

The arXiv preprint 2606.09997 introduces a six-parameter fitting function for median mass accretion rates (MARs) that depends only on peak height ν, effective spectral index n_eff, and growth rate α_eff, derived from both dark-matter-only and hydrodynamical runs spanning ΛCDM and Einstein-de Sitter cosmologies between z=0 and z=14. This approach improves on the classic Lacey & Cole (1993) formation-time formula by anchoring one parameter to its physical value and incorporating n_eff dependence, yielding higher accuracy at low masses and high redshifts. Simulations underpinning the fit contain no quoted halo count or volume, limiting direct assessment of statistical robustness; the authors themselves note that baryonic processes remain effectively invisible to MARs, an assumption that may break at z>10 where feedback alters inner density profiles. Placed against Behroozi et al. (2019) empirical accretion tracks from observed stellar-mass functions, the new model predicts systematically earlier formation for 10^10 M⊙ halos at z≈8, offering a testable link to JWST reports of unexpectedly massive galaxies. The Colossus implementation further enables rapid forward modeling of UV luminosity functions, exposing a missing connection in prior semi-analytic codes that treated accretion as purely mass- and redshift-dependent. Limitations include the absence of warm-dark-matter or self-interacting variants and the use of median rather than full probability distributions, which may mask rare rapid-growth events driving starbursts.