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

A constant early dark energy (EDE) component contributing a fraction f(EDE) (z(c)) similar to 10% of the energy density of the universe around z(c) similar or equal to 3500 and diluting as or faster than radiation afterwards, can provide a simple resolution to the Hubble tension, the similar to 5 sigma discrepancy-in the Lambda CDM context-between the H-0 value derived from early- and late-universe observations. However, it has been pointed out that including Large-Scale Structure (LSS) data, which are in similar to 3 sigma tension with Lambda CDM and EDE cosmologies, might break some parameter degeneracy and 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(EDE) (z(c)), we report in agreement with past work a similar to 2 sigma preference for nonzero f(EDE) (z(c)) from Planck CMB data alone, while the tension with the local H-0 measurement from SH0ES is reduced below 2 sigma. Adding BAO, FS and SNIa does not affect this conclusion, while the inclusion of a prior on H-0 from SH0ES increase the preference for EDE over Lambda CDM to the similar to 3.6 sigma level. After checking the EDE nonlinear matter power spectrum as predicted by standard semi-analytical algorithms via a dedicated set of N-body simulations, we test the 1-parameter EDE cosmology against WL data. We find that it does not significantly worsen the fit to the S-8 measurement as compared to Lambda CDM, and that current WL observations do not exclude the EDE resolution to the Hubble tension. We also caution against the interpretation of constraints obtained from combining statistically inconsistent datasets within the Lambda CDM cosmology. In light of the CMB lensing anomalies, we show that the lensing-marginalized CMB data also favor nonzero f(EDE)(z(c)) at similar to 2 sigma, predicts H-0 in 1.4 sigma agreement with SH0ES and S-8 in 1.5 sigma and 0.8 sigma agreement with KiDS-VIKING and DES respectively. There still exists however a similar to 2.5 sigma tension with the joint results from KiDS-VIKING and DES. With an eye on Occam's razor, we finally discuss promising extensions of the EDE cosmology that could allow us to fully restore cosmological concordance.