Reionization constraints on primordial magnetic fields

We study the impact of the extra density fluctuations induced by primordial magnetic fields on the reionization history in the redshift range: 6 < z < 10. We perform a comprehensive Markov chain Monte Carlo (MCMC) physical analysis allowing the variation of parameters related to primordial magnetic fields (strength, B0, and power-spectrum index |$n_{\scriptscriptstyle \rm B}$|⁠), reionization and Λ cold dark matter cosmological model. We find that magnetic field strengths in the range: B0 ≃ 0.05–0.3 nG (for nearly scale-free power spectra) can significantly alter the reionization history in the above redshift range and can relieve the tension between the Wilkinson Microwave Anisotropy Probe and quasar absorption spectra data. Our analysis puts upper limits on the magnetic field strength B0 < 0.358, 0.120 and 0.059 nG (95 per cent c.l.) for |$n_{\scriptscriptstyle \rm B} = -2.95, -2.9 \hbox{ and }-2.85$|⁠, respectively. These represent the strongest magnetic field constraints among those available from other cosmological observables.