Can early dark energy be probed by the high-redshift galaxy abundance?

The analysis of the cosmic microwave background data acquired by the Atacama Cosmology Telescope and the large-scale ($\ell \lesssim 1300$) Planck Telescope show a preference for the early dark energy (EDE) theory, which was set to alleviate the Hubble tension of the $\Lambda$ cold dark matter ($\Lambda$CDM) model by decreasing the sound horizon $r_{s}$, and gives $H_{0} \approx 72$ km s$^{-1}$ Mpc$^{-1}$. However, the EDE model is commonly questioned for exacerbating the $\sigma _8$ tension on top of the $\Lambda$CDM model, and its lack of preference from the late-time matter power spectrum observations, e.g. Baryon Oscillation Spectroscopic Survey. In light of the current obscurities, we inspect if the high redshift galaxy abundance, i.e. stellar mass function/density and luminosity function, can independently probe the EDE model. Our result shows that, compared to $\Lambda$CDM, the EDE model prediction at $z\gt 10$ displays better consistency with the unexpectedly high results observed by the JWST. At lower redshift, the EDE model only fits the most luminous/massive end, with the majority of the data presenting better consistency with $\Lambda$CDM, implying that adding an extra luminosity/mass-sensitive suppression mechanism of the galaxy formation is required for EDE to explain all data around $z\sim 7-10$.