Cosmological Magnetic Fields vs . CMB

I present a short review of the effects of a cosmological magnetic field on the CMB temperature and polarization anisotropies. Various possibilities for constraining the magnetic field amplitude are discussed. Cosmological primordial seed magnetic fields were proposed to explain the existence of observed ∼ 10 −6 G magnetic fields in galaxies and clusters (see, e.g., Widrow 2002, Gio-vaninni 2003, and references therein). To preserve approximate spatial isotropy a seed vector magnetic field has to be small and hence can be treated as a first order term in perturbation theory. If the energy density parameter of a primordial magnetic field, Ω B = B 2 /(4πρ cr) (where ρ cr is the critical density), is five or six of order of magnitude less than that of the radiation (photons), Ω B ∼ 10 −6 − 10 −5 Ω γ , this is still of the order of the current accuracy of CMB measurements (Bennett et al. 2003), so we might expect that such a field strength (B ∼ 10 −8 − 10 −9 Gauss) could leave detectable traces on CMB temperature or polarization anisotropies. Primordial magnetic fields could be generated during early epochs of the Universe, such as during inflation, or the electroweak phase transition, or might be generated by primordial turbulence (for reviews see Grasso and Rubinstein 2001, Widrow 2002, Giovaninni 2003). Cosmological magnetic fields induce scalar (density), vector (vorticity) and tensor (gravitational waves) fluctuations, and through them influence the CMB temperature and polarization anisotropies (see Mack et al. 2002 and references therein). Hence precise CMB measurements (Bennett et al. 2003) can be used to constrain primordial magnetic fields. An interesting possibility is to consider the rotation of the CMB polarization plane due to the Faraday effect (Kosowsky and Loeb 1996). The simplest illustrative case to consider is a homogeneous magnetic field (Giovaninni and Shaposhnikov 1998), which generates magnetosonic and Alfvén waves. Due to the