CERN-TH-2018-093 Probing large-scale magnetism with the Cosmic Microwave Background Massimo Giovannini 1 Department of Physics, Theory Division, CERN, 1211 Geneva 23, Switzerland INFN, Section of Milan-Bicocca, 20126 Milan, Italy Abstract Prior to photon decoupling magnetic random fields of comoving intensity in the nano- Gauss range distort the temperature and the polarization anisotropies of the microwave background, potentially induce a peculiar B-mode power spectrum and may even generate a frequency-dependent circularly polarized V -mode. We critically analyze the theoretical foundations and the recent achievements of an interesting trialogue involving plasma physics, general relativity and astrophysics. arXiv:1712.07598v2 [astro-ph.CO] 3 May 2018 1Electronic address:
[email protected] Contents 1 A magnetized Universe 3 1.1 History, orders of magnitude and units . 3 1.2 Magnetic fields in galaxies . 5 1.3 Magnetic fields in clusters . 6 1.4 Magnetic fields at the largest scales . 7 1.5 Magnetic random fields and CMB observables . 9 2 The pre-decoupling plasma 12 2.1 Plasma parameters . 12 2.2 Gravitating plasmas . 13 2.2.1 Evolution of the electromagnetic fields in curved space . 15 2.2.2 Comoving and physical descriptions . 16 2.2.3 The approximate temperature of the plasma . 17 2.3 Relativistic fluctuations of the geometry . 18 2.3.1 Scalar, vector and tensor modes . 19 2.3.2 Gauge-invariant normal modes of the system . 20 2.4 The concordance paradigm . 21 2.4.1 The pivotal parameters . 21 2.4.2 Neutrinos, photons and baryons . 22 2.4.3 Large-scale inhomogeneities .