Magnetized CMB anisotropies

Possible effects of large-scale magnetic fields on the Cosmic Microwave Background (CMB) are reviewed. Depending on the specific branch of the spectrum of plasma excitations, magnetic fields are treated either within a two-fluid plasma description or within an effective (one-fluid) approach. The uniform field approximation is contrasted with the fully inhomogeneous field approximation. It is argued that the interplay between CMB physics and large-scale magnetic fields will represent a rather interesting cross-disciplinary arena along the next few years. e-mail address: [email protected] 1 Why CMB anisotropies could be magnetized? Simplified magneto-hydrodynamical estimates imply that the magnetic diffusivity length scale2 in the interstellar medium is of the order of the astronomical unit. On the other hand, magnetic fields are present over much larger length-scales so that there seems to be rather compelling evidence that galaxies, clusters and possibly super-clusters are all magnetized. The question that arises naturally in this context concerns the possible effects of large-scale magnetic fields on the Cosmic Microwave Background (CMB). In the last fifty years various cosmological mechanisms for the origin of large scale magnetic fields have been proposed. While different mechanisms rely on diverse physical assumptions some general features can be identified: • the majority of the cosmological mechanisms imply the existence of large-scale magnetic fields after equality (but before decoupling); • the magnetic field present after equality is, according to the mentioned mechanisms, fully inhomogeneous; • the typical amplitudes and length-scales of the magnetic field are characteristic of the given model. The first possibility we can think of implies that magnetic fields are produced, at a given epoch in the life of the Universe, inside the Hubble radius, for instance by a phase transition or by any other phenomenon able to generate a charge separation and, ultimately, an electric current. In this context, the correlation scale of the field is much smaller that the typical scale of the gravitational collapse of the proto-galaxy which is of the order of the Mpc. In fact, if the Universe is decelerating and if the correlation scale evolves as the scale factor, the Hubble radius grows much faster than the correlation scale. Of course, one might invoke the possibility that the correlation scale of the magnetic field evolves more rapidly than the scale factor. A well founded physical rationale for this occurrence is what is normally called inverse cascade, i.e. the possibility that magnetic (as well as kinetic) energy density is transferred from small to large scales. This implies, in real space, that (highly energetic) small scale magnetic domains may coalesce to form magnetic domains of smaller energy but over larger scales. In the best of all possible situations, i.e. when inverse cascade is very effective, it seems rather hard to justify a growth of the correlation scale that would eventually end up into a Mpc scale at the onset of gravitational collapse. In Fig. 1 we report a schematic illustration of the evolution of the Hubble radius RH and of The magnetic diffusivity length is the typical scale below which magnetic fields are diffused because of the finite value of the conductivity of the (interstellar) medium.