Revisiting constraints on primordial magnetic fields from spectral distortions of cosmic microwave background

The magneto-hydrodynamic decay of primordial magnetic fields can distort the black-body spectrum of the cosmic microwave background (CMB) by draining magnetic energy into thermal plasmas and photons. The current limits on CMB distortion place constraints on small-scale primordial magnetic fields. The constraints crucially depend on the decay laws of primordial magnetic fields. Recent numerical simulations reveal that non-linear effects play a siginificant role in the magnetic field decay although these effects are neglected in previous works. In this paper, by adopting a reconnection-driven turbulent decay as a non-linear evolution model, we demonstrate the potential impact of non-linear effects on CMB spectral distortions. The reconnection-driven turbulent decay model is an analytical description which provides the consistent results with numerical simulation. Our results rule out magnetic fields with shorter coherence lengths. While the result is independent of the spectral index of the magnetic energy spectrum, it is influenced by the magnetic helicity fraction.