Primordial magnetic field as a common solution of nanohertz gravitational waves and the Hubble tension

Understand

The origin of interstellar and intergalactic magnetic fields remains largely unknown.

• One possibility is that they are related to the primordial magnetic fields (PMFs) produced by, for instance, the phase transitions of the early Universe.
• In this paper, we show that the PMF-induced turbulence generated at around the QCD phase transition epoch--the characteristic magnetic field strength $B_{\rm ch}^* \sim \mathcal{O}(1)~\rm{\mu G}$ and coherent length scale $\ell_{\rm ch}^* \sim \mathcal{O}(1)~\rm{pc}$--can naturally accommodate nanohertz gravitational waves reported by pulsar timing array (PTA) collaborations.
• Moreover, the evolution of the PMFs to the recombination era with the form of $B_{\rm ch}\sim \ell_{\rm ch}^{-\alpha}$ can induce baryon density inhomogeneities, alter the recombination history, and alleviate the tension of the Hubble parameter $H_0$ and the matter clumpiness parameter $S_8$ between early- and late-time measurements for $0.88\leq \alpha \leq 1.17$ (approximate 95\% credible region based on three PTA likelihoods).