NANOGrav signal from magnetohydrodynamic turbulence at the QCD phase transition in the early Universe

The NANOGrav Collaboration has recently reported evidence for the existence of a stochastic gravitational wave background in the 1–100 nHz frequency range. We argue that such a background could have been produced by magnetohydrodynamic (MHD) turbulence at the QCD scale. From the NANOGrav measurement, one can infer the magnetic field parameters: a comoving field strength close to microGauss and a correlation length close to 10% of the Hubble radius at the QCD phase transition epoch. We point out that the turbulent decay of a nonhelical magnetic field with such parameters leads to a magnetic field at the recombination epoch, which would be sufficiently strong to provide a solution to the Hubble tension problem, as recently proposed. We also show that the MHD turbulence interpretation of the NANOGrav signal can be tested via measurements of the relic magnetic field in the voids of the large scale structure, with gamma-ray telescopes like CTA.

Figure 1

Spectra of the GW energy density for GW signal from magnetic fields generated at the QCD phase transition, compared to IPTA, SKA [16], and LISA [17] sensitivities. Green and orange wedges correspond to the allowed range of slopes and normalization of the GW density from the broken power law and power-law fits to the NANOGrav cross-power spectral density [14]. Red wedge is the result of EPTA (3rd Annual Assembly GdR “Ondes Gravitationnneles,” [18]). Red solid, dashed and dotted curves show broken power-law type models of the type derived in Ref. [19] for different magnetic field forcing scales.

Figure 2

Constraints on cosmological magnetic fields, compared to the NANOGrav result [14] interpreted as evidence for the detection of a primordial magnetic field. The sensitivities of GW detectors [12, 16, 17] are shown by the upper blue shading for a sharply peaked SGWB (thick solid), a SGWB with $k^1$ slope (dashed thin), and with $k^3$ slope (thin solid lines). The lower light blue shading shows the sensitivity of CTA [2, 6, 37]. The lower bounds with different degrees of grey shading show the Fermi/LAT lower bound on the intergalactic magnetic field from timing of the blazar signal (darker), and from the search of extended emission (lighter) [8]. The CMB upper bound is from the analysis of [2, 4]. The suggested detection of a SGWB is marked by the red circle. Red shading corresponds to the uncertainty range. The green line shows end points of the cosmological evolution of primordial magnetic fields, at the recombination epoch [2, 46]. The red interval on the green line shows the possible detection from Ref. [36]. The rose arrow shows the evolutionary path via compressible turbulent decay [2]. The black dashed and dotted lines show the comoving Hubble radius and the largest processed eddy at the QCD phase transition.