Early dark energy resolution to the Hubble tension in light of weak lensing surveys and lensing anomalies

Early Dark Energy (EDE) contributing a fraction $f_{\rm EDE}(z_c)\sim 10 \%$ of the energy density of the universe around $z_c\simeq 3500$ and diluting as or faster than radiation afterwards, can provide a resolution to the Hubble tension, the $\sim 5\sigma$ discrepancy between the $H_0$ value derived from early- and late-universe observations within $\Lambda$CDM. However, it has been pointed out that Large-Scale Structure (LSS) data, which are in $\sim3\sigma$ tension with $\Lambda$CDM and EDE cosmologies, might alter these conclusions. We reassess the viability of the EDE against a host of high- and low-redshift measurements, by combining LSS observations from recent weak lensing (WL) surveys with CMB, Baryon Acoustic Oscillation (BAO), growth function (FS) and Supernova Ia (SNIa) data. Introducing a model whose only parameter is $f_{\rm EDE}(z_c)$, we report a $\sim 2\sigma$ preference for non-zero $f_{\rm EDE}(z_c)$ from Planck data alone and the tension with SH0ES is reduced below $2\sigma$. Adding BAO, FS and SNIa does not affect this result, while the inclusion of a prior on $H_0$ from SH0ES increase the preference for non-zero EDE to $\sim3.6\sigma$. After checking the EDE non-linear matter power spectrum predicted by standard semi-analytical algorithms via a set of $N$-body simulations, we show that current WL data do not rule out EDE. We also caution against the interpretation of constraints obtained from combining statistically inconsistent data sets within the $\Lambda$CDM cosmology. In light of the CMB lensing anomalies, we show that the lensing-marginalized CMB data also favor non-zero $f_{\rm EDE}(z_c)$ at $\sim2\sigma$, predicts $H_0$ in $1.4\sigma$ agreement with SH0ES and $S_8$ in $1.5\sigma$ ($0.8\sigma$) agreement with KV (DES) data. Alternatively, we discuss promising extensions of the EDE cosmology that could allow to fully restore cosmological concordance.