Early JWST photometry revealed candidate galaxies at redshift z≃7z\simeq7–10 whose cumulative stellar mass density exceeds standard Λ\LambdaCDM predictions by about an order of magnitude even at maximal star-formation efficiency. Biagetti, Franciolini & Riotto (2023) showed that primordial non-Gaussianity (NG) can boost the required halo abundances only if it is large, positive, and switched on sharply at the small scales that CMB and galaxy-survey bounds do not directly probe, and they listed the unresolved issues any such explanation must face: observational systematics of the candidate sample, the validity of the Edgeworth-truncated halo mass function at large skewness, the existence of a natural inflationary realization consistent with other probes, halo-mass-function fitting-formula systematics, and unexplored parameter degeneracies. The open problem is the end-to-end viability assessment: determine whether such NG, anchored to the now partially spectroscopically controlled abundance measurements, can reconcile observation with theory under a validated halo-mass-function treatment, an explicit inflationary model, and joint marginalization over cosmological and astrophysical parameters. Later literature (2023–2026) has reduced and partially anchored the observational tension, tightened UV-luminosity-function limits on small-scale features, and built simulation tools for scale-dependent NG, but no work has closed the question; the non-Gaussianity channel remains open, though under increasing pressure from astrophysical explanations.

Background

The James Webb Space Telescope (JWST), the current flagship infrared observatory, began releasing extragalactic survey data in 2022. Within weeks, photometric searches reported a population of surprisingly luminous and massive galaxy candidates at redshift z≳8z\gtrsim8, when the Universe was under roughly 600 million years old. Labbé et al. (2023) quantified the surprise: from 14 candidates at 7<z<117<z<11 in the CEERS survey (the JWST Cosmic Evolution Early Release Science survey) they inferred a cumulative comoving stellar mass density ρ∗(>1010M⊙,z≃10)≃1.3−0.6+1.1×106 M⊙ Mpc−3\rho_*(>10^{10}M_\odot,z\simeq10)\simeq1.3^{+1.1}_{-0.6}\times10^{6}\,M_\odot\,{\rm Mpc}^{-3} (the total mass in stars per comoving volume above the stated threshold; a comoving quantity is measured in present-day coordinates that expand with the Universe), about 50 times the prediction of the standard cosmological model (Λ\LambdaCDM: a cosmological constant plus cold dark matter) even under the maximally conservative assumption that every baryon in a collapsed dark-matter halo turns into stars. Several caveats applied immediately: the candidates had only photometric redshifts (redshifts estimated by fitting spectral-energy-distribution templates to multi-band images, a method untested at these depths), and their stellar masses depended on assumptions about the initial mass function (IMF, the distribution of stellar birth masses), dust attenuation, nebular-line contamination, and possible active-galactic-nucleus (AGN) light.

One route to boost early halo abundances without changing late-time physics is to modify the primordial perturbations themselves. Primordial non-Gaussianity (NG) denotes deviations of the initial curvature perturbation from a Gaussian random field, conventionally parameterized by an fNLf_{\rm NL}-type amplitude of the bispectrum (three-point function). Positive local-type NG adds positive skewness to the density probability distribution and enhances the exponential high-mass tail of the halo mass function (HMF), the comoving number density of dark-matter halos per unit mass, which is usually taken from fitting formulas calibrated on Gaussian N-body simulations, e.g. Tinker et al. (2010) or Sheth & Tormen (2002). The standard analytic NG correction is a leading-order Edgeworth expansion (a Gram–Charlier-type series of the density probability density function): the HMF is multiplied by a factor built from the skewness S3S_3 of the smoothed density field, and higher cumulants (kurtosis, etc.) are neglected — an approximation valid only for weak NG.

Biagetti, Franciolini & Riotto (2023) tested this route against the JWST data. Large-scale constraints forbid large NG on the scales probed by the cosmic microwave background (CMB, the relic radiation of the early Universe, mapped to high precision by the Planck satellite) and galaxy surveys (∣fNL∣≲10|f_{\rm NL}|\lesssim10 from Planck, ≲26\lesssim26 from quasar clustering measured by eBOSS, the extended Baryon Oscillation Spectroscopic Survey, at k≲0.3 h Mpc−1k\lesssim0.3\,h\,{\rm Mpc}^{-1}), and Hubble Space Telescope (HST) ultraviolet luminosity functions (UVLFs, the galaxy number counts versus UV luminosity that trace star formation rather than stellar mass) bound small-scale NG to fNL≲500f_{\rm NL}\lesssim500 if NG is already active at kcut∼0.15 h Mpc−1k_{\rm cut}\sim0.15\,h\,{\rm Mpc}^{-1} (Sabti, Muñoz & Blas 2021), with bounds loosening at larger kcutk_{\rm cut}. The authors therefore considered strongly scale-dependent NG that switches on only at the comoving wavenumbers (spatial frequencies of the perturbations, in units of inverse megaparsecs with the Hubble constant scaled as h=H0/100 km s−1 Mpc−1h=H_0/100\,{\rm km\,s^{-1}\,Mpc^{-1}}) k∼1 h Mpc−1k\sim1\,h\,{\rm Mpc}^{-1} corresponding to ∼1011M⊙\sim10^{11}M_\odot halos, including a step (sharp cutoff in kk) and a narrow bump. Sharp cutoffs of this kind can arise in multi-field inflation when a spectator field undergoes a mass transition at the corresponding epoch (Riotto & Sloth 2011). Their conclusions: only large, sharply scale-dependent NG helps; the required skewness is so large that the Edgeworth truncation neglecting kurtosis becomes questionable (their footnote 3); the Tinker-versus-Sheth–Tormen baseline choice alone shifts the required fNLf_{\rm NL} by a factor of order two; raising σ8\sigma_8 (the amplitude of matter fluctuations) to ≳0.9\gtrsim0.9 instead is excluded by Planck; and a complete degeneracy analysis and the observational systematics remain open. Since 2024, compact red AGN-like sources dubbed Little Red Dots (LRDs) have been identified as a contaminant of massive high-redshift samples, adding to the systematics inventory.

Problem Statement

Determine, end to end, whether primordial non-Gaussianity can reconcile the JWST-inferred abundances of massive galaxies at z≃7z\simeq7-10 (e.g. the cumulative stellar mass density above 1010M⊙10^{10}M_\odot) with existing bounds. The overarching objective is a defensible viability verdict on the non-Gaussian initial-conditions explanation, and it jointly requires: (i) an observational anchor in which the target abundance itself is controlled against its systematics — spectroscopic confirmation status, photometric-redshift failures and dusty interlopers, AGN/Little Red Dot contamination, initial-mass-function, dust, nebular-line, and star-formation-scatter uncertainties; (ii) a halo-mass-function treatment whose non-Gaussian correction is shown valid in the required regime of large small-scale skewness S3S_3 — beyond the leading Edgeworth truncation that neglects kurtosis and higher cumulants — and whose Gaussian baseline (Tinker versus Sheth–Tormen type fits) is controlled at high redshift and low halo mass, given the order-unity shifts it induces in the required fNLf_{\rm NL}; (iii) an explicit inflationary realization of the scale-dependent NG that switches on only at the small scales (k≳1 h Mpc−1k\gtrsim1\,h\,{\rm Mpc}^{-1}) not directly constrained by Planck CMB and eBOSS bounds, together with an assessment of its theoretical naturalness and its consistency with other probes, in particular HST/JWST UV luminosity functions and any small-scale CMB or secondary-anisotropy limits; and (iv) a joint exploration of cosmological and astrophysical parameter degeneracies — including σ8\sigma_8, star-formation efficiency and halo-to-stellar-mass relations, scatter in star formation, and the non-Gaussianity parameters themselves — establishing whether any allowed combination of parameter shifts explains the abundances without non-Gaussianity, and, conversely, whether adding non-Gaussianity produces a consistent overall picture including the observed redshift evolution between z≃8z\simeq8 and z≃10z\simeq10. These components are jointly necessary: each discharges a distinct failure mode of the non-Gaussianity explanation.

References

  1. Matteo Biagetti, Gabriele Franciolini, Antonio Riotto, 'High-redshift JWST Observations and Primordial Non-Gaussianity', The Astrophysical Journal 944, 113 (2023), doi:10.3847/1538-4357/acb5ea, https://doi.org/10.3847/1538-4357/acb5ea (preprint arXiv:2210.04812)
  2. Ivo Labbé, Pieter van Dokkum, Erica Nelson, Rachel Bezanson, Katherine A. Suess, Joel Leja, Gabriel Brammer, Katherine Whitaker, Elijah Mathews, Mauro Stefanon, Bingjie Wang, 'A population of red candidate massive galaxies ~600 Myr after the Big Bang', Nature 616, 266-269 (2023), doi:10.1038/s41586-023-05786-2, https://doi.org/10.1038/s41586-023-05786-2
  3. Nashwan Sabti, Julian B. Muñoz, Diego Blas, 'First constraints on small-scale non-Gaussianity from UV galaxy luminosity functions', Journal of Cosmology and Astroparticle Physics 2021(01), 010 (2021), doi:10.1088/1475-7516/2021/01/010, https://doi.org/10.1088/1475-7516/2021/01/010
  4. Antonio Riotto, Martin S. Sloth, 'Strongly scale-dependent non-Gaussianity', Physical Review D 83, 041301 (2011), doi:10.1103/PhysRevD.83.041301, https://doi.org/10.1103/PhysRevD.83.041301
  5. Jeremy L. Tinker, Brant E. Robertson, Andrey V. Kravtsov, Anatoly Klypin, Michael S. Warren, Gustavo Yepes, Stefan Gottlöber, 'The Large-Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests', The Astrophysical Journal 724, 878-886 (2010), doi:10.1088/0004-637X/724/2/878, https://doi.org/10.1088/0004-637X/724/2/878
  6. Ravi K. Sheth, Giuseppe Tormen, 'An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier', Monthly Notices of the Royal Astronomical Society 329, 61-75 (2002), doi:10.1046/j.1365-8711.2002.04950.x, https://doi.org/10.1046/j.1365-8711.2002.04950.x
  7. Nashwan Sabti, Julian B. Muñoz, Marc Kamionkowski, 'Insights from HST into Ultramassive Galaxies and Early-Universe Cosmology', Physical Review Letters 132, 061002 (2024), doi:10.1103/PhysRevLett.132.061002, https://doi.org/10.1103/PhysRevLett.132.061002 (preprint arXiv:2305.07049)
  8. Tao Wang, Hanwen Sun, Luwenjia Zhou, Ke Xu, Cheng Cheng, Zhaozhou Li, Yangyao Chen, H. J. Mo, Avishai Dekel, Tiancheng Yang, Yijun Wang, Longyue Chen, Xianzhong Zheng, Zheng Cai, David Elbaz, Y.-S. Dai, J.-S. Huang, 'JWST/MIRI reveals the true number density of massive galaxies in the early Universe', The Astrophysical Journal Letters 988, L35 (2025), doi:10.3847/2041-8213/adebe7, https://doi.org/10.3847/2041-8213/adebe7 (preprint arXiv:2403.02399)
  9. Ben Forrest, M. C. Cooper, Adam Muzzin, Gillian Wilson, Danilo Marchesini, Ian McConachie, Percy Gomez, Marianna Annunziatella, Z. Cemile Marsan, Joey Braspenning, Wenjun Chang, Gabriella de Lucia, Fabio Fontanot, Michaela Hirschmann, Dylan Nelson, Annalisa Pillepich, Joop Schaye, Stephanie M. Urbano Stawinski, Mauro Stefanon, Lizhi Xie, 'MAGAZ3NE: Massive, Extremely Dusty Galaxies at z~2 Lead to Photometric Overestimation of Number Densities of the Most Massive Galaxies at 3<z<4', The Astrophysical Journal 977, 51 (2024), doi:10.3847/1538-4357/ad8b1c, https://doi.org/10.3847/1538-4357/ad8b1c (preprint arXiv:2404.19018)
  10. Chloe M. Cheng, Martje Slob, Mariska Kriek, Aliza G. Beverage, Pieter G. van Dokkum, Rachel Bezanson, Gabriel Brammer, Charlie Conroy, Anna de Graaff, Elham Eftekhari, Robert Feldmann, Wout M. Goesaert, Meng Gu, Joel Leja, Brian Lorenz, Pavel E. Mancera Piña, Ignacio Martín-Navarro, Andrew B. Newman, Sedona H. Price, Alice E. Shapley, Piyush Sharda, Katherine A. Suess, Arjen van der Wel, Daniel R. Weisz, 'Hidden mass in early galaxies revealed by bottom-heavy initial mass functions' (2026), doi:10.1038/s41550-026-02932-4, https://doi.org/10.1038/s41550-026-02932-4 (preprint arXiv:2601.20864)
  11. Leonardo Comini, Sunny Vagnozzi, Abraham Loeb, 'Dark energy, spatial curvature, and star formation efficiency from JWST photometric and spectroscopic high-redshift galaxies', Journal of High Energy Astrophysics 53, 100626 (2026), doi:10.1016/j.jheap.2026.100626, https://doi.org/10.1016/j.jheap.2026.100626 (preprint arXiv:2604.13866)
  12. Sandeep Kumar Acharya, 'Probing inflationary features with galaxy ultraviolet luminosity function observables', arXiv:2602.23913 (2026), https://arxiv.org/abs/2602.23913
  13. Soubhik Kumar, Neal Weiner, 'Early Galaxies from Rare Inflationary Processes and JWST Observations', Physical Review D 112, 063560 (2025), doi:10.1103/ywfw-4rhn, https://doi.org/10.1103/ywfw-4rhn (preprint arXiv:2502.08701)
  14. Marco Baldi, Emanuele Fondi, Dionysios Karagiannis, Lauro Moscardini, Andrea Ravenni, William R. Coulton, Gabriel Jung, Michele Liguori, Marco Marinucci, Licia Verde, Francisco Villaescusa-Navarro, Benjamin D. Wandelt, 'Cosmological simulations of scale-dependent primordial non-Gaussianity', Journal of Cosmology and Astroparticle Physics 2024(11), 053 (2024), doi:10.1088/1475-7516/2024/11/053, https://doi.org/10.1088/1475-7516/2024/11/053 (preprint arXiv:2407.06641)
  15. Clément Stahl, Benoit Famaey, Rodrigo Ibata, Katarina Kraljic, Fabien Castillo, 'A cosmic degeneracy story: structure formation with warm dark matter and scale-dependent primordial non-Gaussianities', arXiv:2501.03672 (2025), https://arxiv.org/abs/2501.03672
  16. Guochao Sun, Claude-André Faucher-Giguère, Christopher C. Hayward, Xuejian Shen, Andrew Wetzel, Rachel K. Cochrane, 'Bursty Star Formation Naturally Explains the Abundance of Bright Galaxies at Cosmic Dawn', The Astrophysical Journal Letters 955, L35 (2023), doi:10.3847/2041-8213/acf85a, https://doi.org/10.3847/2041-8213/acf85a (preprint arXiv:2307.15305)
  17. Xuejian Shen, Mark Vogelsberger, Michael Boylan-Kolchin, Sandro Tacchella, Rohan P. Naidu, 'Early Galaxies and Early Dark Energy: A Unified Solution to the Hubble Tension and Puzzles of Massive Bright Galaxies revealed by JWST', Monthly Notices of the Royal Astronomical Society 533, 3923-3936 (2024), doi:10.1093/mnras/stae1932, https://doi.org/10.1093/mnras/stae1932 (preprint arXiv:2406.15548)
  18. Mattéo Blamart, Adrian Liu, Robert Brandenberger, Julian B. Muñoz, Bryce Cyr, 'UV Luminosity Functions from HST and JWST: A Possible Resolution to the High-Redshift Galaxy Abundance Puzzle and Implications for Cosmic Strings', arXiv:2512.09980 (2025), https://arxiv.org/abs/2512.09980