Lecture notes released as a preprint (arXiv:2604.01445v1, not yet peer-reviewed) from the 54th Saas-Fee Advanced Course distill current theory on galaxy formation during the first billion years of cosmic time, aimed at early-career researchers. These notes review cosmological structure formation in the Lambda Cold Dark Matter (LCDM) framework, properties of dark matter halos at redshifts z greater than or equal to 6, and evaluate whether JWST data fundamentally challenges the standard model. The author concludes that while puzzles exist, no observations to date require abandoning LCDM, though baryonic processes in simulations need refinement.

This preprint synthesizes theoretical tools like halo mass functions and semi-analytic models but goes beyond by addressing translation of simulation outputs to observables such as UV luminosity. However, it underplays the cumulative weight of multiple independent JWST programs. For example, the JADES survey (Eisenstein et al., arXiv:2306.02468) and CEERS (Finkelstein et al., arXiv:2306.05422) have revealed a higher-than-expected abundance of UV-bright galaxies at z~8-13. These are not single-object anomalies but population-level tensions: the bright end of the luminosity function exceeds predictions from most pre-JWST simulations by factors of several. A third source, the theoretical review by Vogelsberger et al. on cosmological simulations (Nature Reviews Physics, 2020, updated in later works), highlights how subgrid physics for star formation and feedback were calibrated primarily on z=0 galaxies, limiting their applicability to the metal-poor, high-density early universe.

What existing coverage often misses is the connection between these 'too bright, too early' galaxies and reionization patterns. Brighter early galaxies could supply the necessary ionizing photons more readily, potentially resolving tensions in reionization timelines rather than exacerbating them. Patterns emerging across JWST datasets suggest bursty star formation in low-mass halos (10^8-10^9 solar masses), where supernova feedback is less effective due to shallow gravitational potentials and low metallicity. This aligns with findings from the FIRE-2 simulation suite, which shows highly variable star formation histories at high redshift.

Genuine analysis reveals these tensions are less about dark matter or cosmology and more about our incomplete modeling of baryons. The preprint correctly notes that cosmic variance in small JWST fields and uncertainties in stellar population synthesis (e.g., assumptions about initial mass functions) could reduce the discrepancy. Limitations include the notes' reliance on existing literature without new simulations or data analysis; JWST samples for the brightest objects remain small (dozens rather than hundreds), making statistical inferences preliminary. Future directions flagged in the notes, such as incorporating radiative transfer and dust physics, are critical.

Current understanding indicates hierarchical structure formation proceeds largely as expected, but galaxy formation efficiency was likely higher in the first billion years, driven by rapid gas accretion and different stellar feedback regimes. This does not upend LCDM but demands next-generation simulations that self-consistently model the multiphase interstellar medium at high redshift.