Résumé
Primordial Magnetic Fields (PMFs), long studied as potential relics of the early Universe, accelerate the recombination process and have been proposed as a possible way to relieve the Hubble tension. However, previous studies relied on simplified toy models. In this study, for the first time, we use the recent high-precision evaluations of recombination with PMFs, incorporating full magnetohydrodynamic (MHD) simulations and detailed Lyman-alpha radiative transfer, to test PMF-enhanced recombination ($b\Lambda$CDM) against observational data from the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and Type Ia supernovae (SN). Focusing on non-helical PMFs with a Batchelor spectrum, we find a preference for present-day total field strengths of approximately 5-10 pico-Gauss. Depending on the dataset combination, this preference ranges from mild ($\sim 1.8\sigma$ with Planck + DESI) to moderate ($\sim 3\sigma$ with Planck + DESI + SH0ES-calibrated SN) significance. The $b\Lambda$CDM has Planck + DESI $\chi^2$ values equal or better than those of the $\Lambda$CDM model while predicting a higher Hubble constant. The favored field strengths align closely with those required for cluster magnetic fields to originate entirely from primordial sources, without the need for additional dynamo amplification or stellar magnetic field contamination. Future high-resolution CMB temperature and polarization measurements will be crucial for confirming or further constraining the presence of PMFs at recombination.