On the Significance of Rare Objects at High Redshift: The Impact of Cosmic Variance

The discovery of extremely luminous galaxies at ultra-high redshifts ($z\gtrsim 8$) has challenged galaxy formation models. Most analyses of this tension have not accounted for the variance due to field-to-field clustering, which causes the number counts of galaxies to vary greatly in excess of Poisson noise. This super-Poissonian variance is often referred to as cosmic variance. Since cosmic variance increases rapidly as a function of mass, redshift, and smaller observing areas, the most massive objects in deep \textit{JWST} surveys are severely impacted by cosmic variance. We construct a simple model, including cosmic variance, to predict the distribution of the mass of the most massive galaxy for different surveys, which increases the tension with observations. The distributions differ significantly from previous predictions using the Extreme Value Statistics formalism, changing the position and shape of the distributions. We test our model using the \texttt{UniverseMachine} simulations, where the predicted effects of cosmic variance are clearly identifiable. We find that the high skew in the distributions of galaxy counts for typical deep surveys imply a high statistical variance on the cosmic variance itself. This impacts the calibration of the cosmic variance, as well as the expected mass of the most massive galaxy. We also find that the impact of cosmic variance dominates the impact of any realistic scatter in the stellar-to-halo-mass relation at $z\gtrsim 12$. It is therefore crucial to accurately account for the impact of cosmic variance in any analysis of tension between early extreme galaxies and galaxy formation models.