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

The Hubble tension and $\sigma_{8}$ tension are two of the major issues of the standard $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model. The analysis of the Cosmic Microwave Background (CMB) data acquired by the Atacama Cosmology Telescope (ACT) and the large-scale ($\ell\lesssim1300$) Planck Telescope manifest their preference for the Early Dark Energy (EDE) theory, which was set to alleviate the Hubble tension 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 (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 and ameliorate the challenges it encounters. Our result shows that the EDE model produces more observable galaxies than $\Lambda$CDM at $z>8$. The LF and SMD, in particular, are consistent with the recent unexpectedly high results observed by the James Webb Space Telescope (JWST), which may posit another observational hint of EDE. This result also implies an efficient suppression mechanism of the galaxy formation rate that leads to the conversion between EDE- and $\Lambda$CDM-like Universe around $z\sim7-10$, and that $\sigma_{8}$ tension could be more of a tension of galaxy evolution than cosmology, hence diminishing its impact on EDE or $\Lambda$CDM theory.