# Extreme Value Statistics of the Halo and Stellar Mass Distributions at High Redshift: are JWST Results in Tension with ΛCDM?

**Authors:** Christopher C. Lovell, Ian Harrison, Yuichi Harikane, Sandro Tacchella, Stephen M. Wilkins  
**arXiv:** [2208.10479](https://arxiv.org/abs/2208.10479)  
**Date:** 2022-08-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2208.10479v2/

## Key points

- The distribution of dark matter halo masses can be accurately predicted in the $\Lambda$CDM cosmology
- Recent measurements of very large galaxy stellar masses at high redshift ($z > 8$) have prompted an investigation into whether these objects are in tension with $\Lambda$CDM
- Extreme value statistics are utilized to generate confidence regions in the mass-redshift plane for the most extreme mass haloes and galaxies
- Tests against numerical models reveal no tension in either their dark matter halo masses or their galaxy stellar masses
- There is a tentative $> 3\sigma$ tension observed with recent observational determinations of galaxy masses at high redshift from both HST and JWST, despite using conservative estimates for the stellar fraction ($f_{\star} \sim 1$)
- This suggests that either these galaxies are indeed in tension with $\Lambda$CDM, or there are unaccounted for uncertainties in their stellar mass or redshift estimates
- The study does not consider the effect of surveys taken from multiple areas of the sky which Behroozi & Silk (2018) argue increases the likelihood of containing outliers
- Observational errors leading to Eddington and Malmquist bias have a much larger impact on predicted probabilities than cosmic variance effect within the extreme value statistics framework
- With upcoming wide field surveys, it is expected that a number of galaxies will be detected that may potentially be in tension with predictions from $\Lambda$CDM or require extreme conversion rates of baryons into stars
- The presented predictions and publicly accessible code aim to provide valuable insights into these potential tensions and aid further research in understanding the effects of region selection.

## Summary

The distribution of dark matter halo masses can be accurately predicted in the $\Lambda$CDM cosmology, allowing for the testing of the underlying cosmological model by examining the presence of a single massive halo or galaxy at a specific redshift. Recent measurements of very large galaxy stellar masses at high redshift ($z > 8$) have prompted an investigation into whether these objects are in tension with $\Lambda$CDM. In this study, extreme value statistics are utilized to generate confidence regions in the mass-redshift plane for the most extreme mass haloes and galaxies. Tests against numerical models reveal no tension in either their dark matter halo masses or their galaxy stellar masses. However, there is a tentative $> 3\sigma$ tension observed with recent observational determinations of galaxy masses at high redshift from both HST and JWST, despite using conservative estimates for the stellar fraction ($f_{\star} \sim 1$). This suggests that either these galaxies are indeed in tension with $\Lambda$CDM, or there are unaccounted for uncertainties in their stellar mass or redshift estimates. It should be noted that this study does not consider the effect of surveys taken from multiple areas of the sky which Behroozi & Silk (2018) argue increases the likelihood of containing outliers. However, it is emphasized that observational errors leading to Eddington and Malmquist bias have a much larger impact on predicted probabilities. Incorporating this cosmic variance effect within the extreme value statistics framework is left as future work. With upcoming wide field surveys, it is expected that a number of galaxies will be detected that may potentially be in tension with predictions from $\Lambda$CDM or require extreme conversion rates of baryons into stars. The presented predictions and publicly accessible code aim to provide valuable insights into these potential tensions and aid further research in understanding the effects of region selection.