Hints of Primordial Magnetic Fields at Recombination and Implications for the Hubble Tension

Primordial Magnetic Fields (PMFs), long studied as relics of the early Universe, accelerate recombination and have been proposed as a way to relieve the Hubble tension. However, previous studies relied on simplified toy models. Here we use recent evaluations of recombination with PMFs, incorporating full magnetohydrodynamic (MHD) simulations and detailed Lyman-alpha radiative transfer, to test PMF-enhanced recombination ($bΛ$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 ($\sim 1.8σ$ with Planck + DESI) to moderate ($\sim 3σ$ with Planck + DESI + SH0ES-calibrated SN) significance. The $bΛ$CDM has Planck + DESI $χ^2$ values equal to or better than $Λ$CDM while predicting a higher Hubble constant. Future high-resolution CMB temperature and polarization measurements will be crucial for confirming or further constraining PMFs at recombination. Field strengths of 5-10 pico-Gauss align closely with those required for cluster magnetic fields to originate entirely from primordial sources, without the need for additional dynamo amplification.