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

Yaoyu Li, Chi Zhang, Ziwei Wang, Mingyang Cui, Yue-Lin Sming Tsai, Qiang Yuan, Yi-Zhong Fan

Published 2023-06-29Version 1

The origin of interstellar and intergalactic magnetic fields is largely unknown, and the primordial magnetic fields (PMFs) produced by, e.g., phase transitions of the early Universe are expected to provide seeds for those magnetic fields. The PMFs affect the evolution of the Universe at an early time, resulting in a series of phenomena. In this work, we show that the PMF-induced turbulence can give rise to nanohertz (nHz) gravitational waves reported by several pulsar timing arrays, including NANOGrav, PPTA, EPTA, and CPTA. Using the nHz gravitational wave data, we obtain the constraints on the characteristic magnetic field strength ($B_{\rm ch}^* \sim \mathcal{O}(1)~\rm{\mu G}$) and coherent length scale ($\ell_{\rm ch}^* \sim \mathcal{O}(1)~\rm{pc}$) of PMFs, assuming a generation temperature of approximately the QCD temperature ($\sim 100$ MeV). In addition, the PMFs which evolve to the recombination era can induce baryon density inhomogeneities, and then alter the ionization process. This naturally results in an alleviation of the tension of the Hubble parameter $H_0$ and the matter clumpiness parameter $S_8$ between early and late-time measurements. Assuming an evolution form of $B_{\rm ch}\sim \ell_{\rm ch}^{-\alpha}$ from the epoch of the production of PMFs to the epoch of recombination, we find $0.91<\alpha<1.08$ (95\% credible region).