Résumé
Phys.Rev.D 107 (2023) 6, 063505 Analyses of the full shape of BOSS DR12 power spectrum using the one-loop prediction from the Effective Field Theory of Large-Scale Structure (EFTBOSS) have led to new constraints on extensions to the$\Lambda$ CDM model, such as Early Dark Energy (EDE) which has been suggested as a resolution to the "Hubble tension". In this paper, we re-assess the constraining power of the EFTBOSS on EDE in light of a correction to the normalization of BOSS window functions. Overall we find that constraints from EFTBOSS on EDE are weakened, and represent a small change compared to constraints from Planck and the conventional BAO/ $f\sigma_8$measurements. The combination of Planck data with EFTBOSS provides a bound on the maximal fractional contribution of EDE$f_{\rm EDE}<0.083$at 95% C.L. (compared to$<0.054$with the incorrect normalization, and$<0.088$without full-shape data) and the Hubble tension is reduced to$2.1\sigma$ . However, the more extreme model favored by an analysis with just data from the Atacama Cosmology Telescope is disfavored by the EFTBOSS data. We also show that the updated Pantheon+ Type Ia supernova analysis can slightly increase the constraints on EDE. Yet, the inclusion of the SN1a magnitude calibration by SH0ES strongly increases the preference for EDE to above$5\sigma$ , yielding$f_{\rm EDE}\sim 0.12^{+0.03}_{-0.02}$around the redshift$z_c=4365^{+3000}_{-1100}$ . Our results demonstrate that EFTBOSS data (alone or combined with Planck data) do not exclude the EDE resolution of the Hubble tension.