Weak Primordial Magnetic Fields and Anisotropies in the Cosmic Microwave Background Radiation

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All cited length scales and magnetic field strengths in this paper are comoving, i.e. the values they would have at the present epoch are given

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Due to efficient CMBR cooling the effective speed of sound is that for an isothermal baryon gas

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In fact, the nonlinearity in C C is only very mild since C C may be well approximated by C ≈ Λ / ( Λ + β e ) C\approx\Lambda/(\Lambda+\beta_{e}) signifying that double photon decay is about one order of magnitude more important than Lyman- α \alpha transitions in producing neutral hydrogen in the ground state

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Though the Lyman- α \alpha photon mean free path is coincidentally of the order of ∼ 1 \sim 1 kpc, i.e. different dense regions are not completely decoupled from each other, the “independent region” approximation is very good since hydrogen formation by Lyman- α \alpha transitions is subdominate (cf. [ 14 ] )

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There are no other plausible candidats for re-creating small-scale inhomogeneity after Silk damping which is volume filling and of magnitude δ ​ ρ / ρ ∼ 1 \delta\rho/\rho\sim 1 known to the authors

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