Can Early Dark Energy be Probed by the High-Redshift Galaxy Abundance?

The analysis of the Cosmic Microwave Background (CMB) data acquired by the Atacama Cosmology Telescope (ACT) and the large-scale ($\mathrm{\ell }\lesssim 1300$) Planck Telescope show a preference for the Early Dark Energy (EDE) theory, which was set to alleviate the Hubble tension of the $\mathrm{\Lambda }$ Cold Dark Matter ($\mathrm{\Lambda }$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 $\mathrm{\Lambda }$CDM model, and its lack of preference from the late-time matter power spectrum observations, e.g., Baryon Oscillation Spectroscopic Survey (BOSS). In light of the current obscurities, we inspect if the high redshift galaxy abundance, i.e., Stellar Mass Function/Density (SMF/SMD) and Luminosity Function (LF), can independently probe the EDE model. Our result shows that, compared to $\mathrm{\Lambda }$CDM, the EDE model prediction at $z>10$ displays better consistency with the unexpectedly high results observed by the James Webb Space Telescope (JWST). At lower redshift, the EDE model only fits the most luminous/massive end, with the majority of the data presenting better consistency with $\mathrm{\Lambda }$CDM, implying that adding an extra luminosity/mass-sensitive suppression mechanism of the galaxy formation is required for EDE to explain all data around $z\sim 7-10$.