Stress Testing $Λ$CDM with High-redshift Galaxy Candidates

TL;DR

The paper tests the ΛCDM expectation that a halo's stellar content cannot exceed its baryonic reservoir by linking the halo mass function to an upper bound on galaxy stellar masses via $M_eta\star=\epsilon f_{ m b}M_{ m halo}$. Using the Sheth–Tormen halo mass function with Planck 2020 parameters, it derives cumulative density limits and confronts them with the JWST high-redshift candidates from Labbé et al., finding that the most massive reported galaxies at $z\sim7-10$ require unrealistically high star-formation efficiencies ($\epsilon\gtrsim0.57$) to be consistent, or else challenge ΛCDM. The results remain robust against small cosmological variations but are in tension with standard baryon budgets, suggesting either extremely rapid early star formation or potential systematic issues; future JWST data will be decisive in confirming or refuting this tension. The work also notes that speculative extensions (e.g., Early Dark Energy) could ease the tension but come with other observational costs, underscoring the importance of spectroscopic follow-up and larger surveys. Overall, the paper provides a concrete, integrative test of the baryon budget in the early universe and highlights a potential, significant challenge to the standard cosmological model if the massive high-redshift candidates are confirmed.

Abstract

Early data from JWST have revealed a bevy of high-redshift galaxy candidates with unexpectedly high stellar masses. An immediate concern is the consistency of these candidates with galaxy formation in the standard cosmological model. In the $Λ$CDM paradigm, the stellar mass ($M_\star$) of a galaxy is limited by the available baryonic reservoir of its host dark matter halo. The mass function of dark matter halos therefore imposes an absolute upper limit on the number density $n(>M_\star,z)$ and stellar mass density $ρ_{\star}(>M_\star,z)$ of galaxies more massive than $M_\star$ at any epoch $z$. Here I show that the most massive galaxy candidates in JWST observations at $z\sim 7-10$ lie at the very edge of these limits, indicating an important unresolved issue with the properties of galaxies derived from the observations, how galaxies form at early times in $Λ$CDM, or within this standard cosmology itself.

Figures (2)

• Figure 1: Limits on the abundance of galaxies as a function of redshift. Curves show the relationship between $M_{\star}$ and $z$ at fixed cumulative halo abundance (left) and fixed $\rho_{\rm b}(>M_{\rm halo})$, or equivalently fixed peak height $\nu$ (right). The most extreme labbe2022 galaxy candidates are shown as blue stars, with uncertainties indicating 68% intervals (symmetric about the median) of the posterior probability distribution. The existence of a galaxy with $M_{\star}$ at redshift $z$ requires that such galaxies have a cumulative comoving number density that is at most the number density shown in the left panel, as those galaxies must reside in host halo of mass $M_{\rm halo}=M_{\star}/(f_{\rm{b}}\,\epsilon)$. The cumulative comoving number density corresponding to an observed $M_{\star}$ will likely be (much) smaller than is indicated here, as the curves are placed on the plot by assuming the physically maximal $\epsilon=1$. For smaller values of $\epsilon$, the curves in each panel move down relative to the points by a factor of $\epsilon$ (as indicated by black downward-facing arrows). The right panel demonstrates that even for the most conservative assumption of $\epsilon=1$, the data points correspond to very rare peaks in the density field, implying a limited baryonic reservoir that is in tension with the measured stellar masses of the galaxies.
• Figure 2: Stellar mass density limits. The comoving stellar mass density contained within galaxies more massive than $M_{\star}$ at $z\approx 9.1$ (left) and $z\approx 7.5$ (right) for three values of the assumed conversion efficiency $\epsilon$ of a halo's cosmic allotment of baryons into stars. Only if all available baryons in all halos with enough baryons to form the galaxies reported by labbe2022 have indeed been converted into stars by that point --- an unrealistic limit --- is it possible produce the stellar mass density in the highest $M_{\star}$ bin at $z\approx 9$ measured by labbe2022 in a typical volume of a $\Lambda$CDM Universe with the Planck 2020 cosmology. Results are similar at $z \approx 7.5$. For more realistic values of $\epsilon$, the required baryon reservoir is substantially larger than the theoretical maximum in this cosmology. When considering shot noise and sample variance errors (which comprise the plotted uncertainties on the labbe2022 data points in each panel), the measurements are consistent with the base $\Lambda$CDM model if $\epsilon > 0.57$, which would still imply incredibly efficient star formation in the high-redshift Universe.