Prospects for distinguishing galaxy evolution models with surveys at redshifts $z \gtrsim 4$

Many semi-empirical galaxy formation models have emerged in recent years to interpret high-$z$ galaxy luminosity functions and make predictions for next generation galaxy surveys. A common approach assumes a "universal" star formation efficiency, $f_{\ast}$, which is independent of cosmic time but strongly dependent on the masses of dark matter halos hosting high-$z$ galaxies. Though this class of models has been very successful in matching observations over much of cosmic history, simple stellar feedback models do predict redshift evolution in $f_{\ast}$, and have become the de-facto recipe in semi-analytic models. In this work, we calibrate a set of universal $f_{\ast}$ and feedback-regulated models to the same set of rest-ultraviolet $z \gtrsim 4$ observations, and find that a rapid, $\sim (1+z)^{-3/2}$ decline in both the efficiency of dust production and duty cycle of star formation are needed to reconcile feedback-regulated models with current observations. By construction, these models remain nearly identical to universal $f_{\ast}$ models in rest-ultraviolet luminosity functions and colours. As a result, the only way to distinguish these competing scenarios is either via (i) improved constraints on the clustering of galaxies -- universal and feedback-regulated models differ in predictions for the typical galaxy bias at the level of $0.1 \lesssim \Delta \langle b \rangle \lesssim 0.3$ over $4 \lesssim z \lesssim 10$ -- or (ii) independent constraints on the dust contents and/or duty cycle of star formation. This suggests that improved constraints on the 'dustiness' and 'burstiness' of high-$z$ galaxies will not merely add clarity to a given model of star formation in high-$z$ galaxies, but rather fundamentally determine our ability to identify the correct model in the first place.