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The cosmic microwave background (CMB) temperature anisotropies from primordial magnetic fields are studied. In addition to the known passive and compensated modes we discuss an inflationary magnetic mode in the curvature perturbation, present when magnetic fields are generated during inflation. This mode is absent if the generation mechanism is causal, e.g. a phase transition. We compute and discuss the effect of this mode on the observed CMB anisotropy spectrum, in comparison with the passive and compensated ones. We find that it dominates the CMB anisotropy, and consequently leads to stronger constraints on the amplitude B1 Mpc and spectral index nB of the magnetic field than what is usually found in CMB analyses from the compensated mode. This happens in particular for spectral indexes nB > --3: the inflationary magnetic mode is always scale invariant; therefore through this mode even a magnetic field with a spectrum which is not scale invariant can leave a detectable signal in the CMB at large scales. [ABSTRACT FROM AUTHOR]

We compute the contribution to the scalar metric perturbations from large-scale magnetic fields which are generated during inflation. We show that apart from the usual passive and compensated modes, the magnetic fields also contribute to the constant mode from inflation. This is different from the causal (postinflationary) generation of magnetic fields where such a mode is absent and it might lead to significant, non-Gaussian CMB anisotropics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]