Primordial magnetic fields (PMFs), being present before the epoch of cosmic recombination, induce small-scale baryonic density fluctuations. These inhomogeneities lead to an inhomogeneous recombination process that alters the peaks and heights of the large-scale anisotropies of the cosmic microwave backround (CMB) radiation. Utilizing numerical compressible MHD calculations and a Monte Carlo Markov chain analysis, which compares calculated CMB anisotropies with those observed by the WMAP and Planck satellites, we derive limits on the magnitude of putative PMFs. We find that the total remaining present day field, integrated over all scales, cannot exceed 47 pG for scale-invariant PMFs and 8.9 pG for PMFs with a violet Batchelor spectrum at 95% confidence level. These limits are more than one order of magnitude more stringent than any prior stated limits on PMFs from the CMB which have not accounted for this effect. *

We extend our recent derivation of the time evolution equations for the energy content of magnetic fields and turbulent motions for incompressible, homogeneous, and isotropic turbulence to include the case of nonvanishing helicity. These equations are subsequently numerically integrated in order to predict the present day primordial magnetic field strength and correlation length, depending on its initial helicity and magnetic energy density. We find that all prior analytic predictions for helical magnetic fields, such as the epoch when they become maximally helical and their subsequent growth of correlation length L $ a 1=3 and decrease of magnetic field strength B $ a À1=3 with scale factor a, are well confirmed by the simulations. An initially fully helical primordial magnetic field is a factor 4 Â 10 4 stronger at the present epoch than its nonhelical counterpart when generated during the electroweak epoch.

We present a derivation of the time evolution equations for the energy content of non-helical magnetic fields and the accompanying turbulent flows from first principles of magnetohydrodynamics in the general framework of homogeneous and isotropic turbulence. This is then applied to the Early Universe, i.e. the evolution of primordial magnetic fields. Numerically integrating the equations we find that most of the energy is concentrated at an integral wave number scale kI where the turbulence turn over time equals the Hubble time. At larger length scales L, or smaller wavenumbers q = 2π/L ≪ kI , independent of the assumed turbulent flow power spectrum, mode-mode coupling tends to develop a small q magnetic field tail from zero with a violet noise slope proportional to the fourth inverse power of L and therefore a scaling for the magnetic field of B ∼ L −5/2 .

One of the most promising ways to probe intergalactic magnetic fields (IGMFs) is through gamma rays produced in electromagnetic cascades initiated by high-energy gamma rays or cosmic rays in the intergalactic space. Because the charged component of the cascade is sensitive to magnetic fields, gamma-ray observations of distant objects such as blazars can be used to constrain IGMF properties. Ground-based and space-borne gamma-ray telescopes deliver spectral, temporal, and angular information of high-energy gamma-ray sources, which carries imprints of the intervening magnetic fields. This provides insights into the nature of the processes that led to the creation of the first magnetic fields and into the phenomena that impacted their evolution. Here we provide a detailed description of how gamma-ray observations can be used to probe cosmic magnetism. We review the current status of this topic and discuss the prospects for measuring IGMFs with the next generation of gamma-ray observatories.