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

TL;DR

This work tests whether primordial magnetic fields (PMFs) present before recombination can accelerate recombination and help resolve the Hubble tension. Using state-of-the-art 3D MHD simulations with detailed Lyman-$\alpha$ transport, the authors derive ionization histories $x_e(z)$ in the presence of non-helical PMFs with a Batchelor spectrum and embed these histories into a Boltzmann solver to compare against Planck CMB, DESI BAO, and SN data. They find a preferred PMF strength of roughly $b_{ m pmf} \sim 3\text{--}10\, {\rm pG}$ at $z=10$ (with recombination values about an order of magnitude larger), translating to an increased inferred $H_0$ of order $69$–$70$ km s$^{-1}$ Mpc$^{-1}$ and partial relief of the $H_0$ and $S_8$ tensions, though results depend on the dataset and suffer from MHD-volume sample variance. The significance of a nonzero PMF ranges from $\sim 1.8\sigma$ to $\sim 3\sigma$, and future high-resolution CMB measurements of the Silk damping tail, plus multi-messenger probes, will be crucial to confirm or constrain PMFs at recombination and clarify their role in cosmic history.

Abstract

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.

Figures (6)

• Figure 1: The marginalized $68$% and $95$% CL for mean $x_e(z)$ runs for Planck+DESI, Planck+DESI+PP+Mb, and the $\Lambda$CDM fit to Planck+DESI. Shown with grey bands are the 68% and 95& CL bands for the $H_0$ measurement by SH0ES Riess:2021jrx, $S_8$ from DES+KiDS KiDS:1000, and $\Omega_m$ from PP Brout:2022vxf.
• Figure 2: The marginalized $68$% and $95$% CL for $b_{\rm pmf}$ and $H_0$ from fits to Planck+DESI+ACT and Planck+DESI+SPT with and without the "SH0ES prior", PP+$M_b$.
• Figure 3: The CMB TT, TE and EE residuals for the best-fit Planck+DESI+PP+$M_b$$b\Lambda$CDM model relative to the $\Lambda$CDM best-fit to Planck+DESI, along with the ACT and SPT band-powers showing the mean values and the one-standard-deviation error bars.
• Figure 4: Relative differences in the ionization histories $x_e(z)$ with respect to the reference $\Lambda$CDM model obtained from MHD simulations with total $z=10$ comoving magnetic field strength of 4.45 pG (top-left), 9.25 pG (top-right), 19.3 pG (bottom-left) and 36.6 pG (bottom-right). The present-day field strength values are approximately 17% lower, while the corresponding values at recombination are given in Table \ref{['tab:brec']} and are a factor of 10 larger. The blue lines are the results from the 5 realizations at each $b_{\rm pmf}$ with the mean ionization history shown in red. The top-right panel includes a 6th realization evaluated at the fiducial cosmological parameters (blue dot) and an alternative set of parameters (green dash), as described in Sec 4.2, demonstrating that changes in $\Delta_e(z)$ due to moderate changes in cosmological parameters are minor compared to the sample variance.
• Figure 5: $\Delta_e(z)$ generated randomly from a Gaussian distribution a mean and covariance corresponding to $b_{\rm pmf}=10$ pG. The figure shows 20 random histories in green and the mean in blue.