Can acoustic and axion-like early dark energy still resolve the Hubble tension?

In this paper, we reassess the ability of the acoustic early dark energy (ADE) and axion-like early dark energy (EDE) models to resolve the Hubble tension in light of the new Pantheon+ and S\(H_0\)ES data on the one hand, and the BOSS LRG and eBOSS QSO data, analyzed under the effective field theory of large-scale structures (ETFofLSS) on the other hand. We find that the Pantheon+ data, which favor a larger \(\Omega_m\) value than the Pantheon data, have a strong constraining power on the ADE model, while the EFTofLSS analysis of the BOSS and eBOSS data only slightly increases the constraints. We establish that the ADE model is now strongly disfavored as a solution to the Hubble tension, with a remaining tension of \(3.6\sigma\) (according to the \(Q_{\rm DMAP}\) metric). In addition, we find that the axion-like EDE model performs better when confronted to the same datasets, with a residual tension of \(2.5\sigma\). This work shows that the Pantheon+ data can have a decisive impact on models which aim to resolve the Hubble tension.