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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 asor faster than radiation afterwards, can provide a resolution to the Hubbletension, the $\sim 5\sigma$ discrepancy between the $H_0$ value derived fromearly- and late-universe observations within $\Lambda$CDM. However, it has beenpointed 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-redshiftmeasurements, by combining LSS observations from recent weak lensing (WL)surveys with CMB, Baryon Acoustic Oscillation (BAO), growth function (FS) andSupernova Ia (SNIa) data. Introducing a model whose only parameter is $f_{\rmEDE}(z_c)$, we report a $\sim 2\sigma$ preference for non-zero $f_{\rmEDE}(z_c)$ 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 theinclusion of a prior on $H_0$ from SH0ES increase the preference for non-zeroEDE to $\sim3.6\sigma$. After checking the EDE non-linear matter power spectrumpredicted by standard semi-analytical algorithms via a set of $N$-bodysimulations, we show that current WL data do not rule out EDE. We also cautionagainst the interpretation of constraints obtained from combining statisticallyinconsistent data sets within the $\Lambda$CDM cosmology. In light of the CMBlensing anomalies, we show that the lensing-marginalized CMB data also favornon-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 cosmologythat could allow to fully restore cosmological concordance.

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