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The NANOGrav collaboration has recently reported evidence for the existenceof a stochastic gravitational wave background in the 1-100 nHz frequency range.We argue that such background could have been produced by magneto-hydrodynamic(MHD) turbulence at the QCD scale. From the NANOGrav measurement one can inferthe magnetic field parameters: comoving field strength close to microGauss anda correlation length close to 10\% of the Hubble radius at the QCD phasetransition epoch. We point out that the turbulent decay of a non-helicalmagnetic field with such parameters leads to a magnetic field at therecombination epoch, which would be sufficiently strong to provide a solutionto the Hubble tension problem, as recently proposed. We also show that the MHDturbulence interpretation of the NANOGrav signal can be tested via measurementsof the relic magnetic field in the voids of the large scale structure, withgamma-ray telescopes like CTA.

NANOGrav signal from MHD turbulence at QCD phase transition in the early universe