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2010

The Evolution of the Large-Scale Tail of Primordial Magnetic Fields

Jedamzik, Karsten, Sigl, Guenter

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Cosmic magnetic fields may be generated during early cosmic phase transition, such as the QCD- or electroweak- transitions.

The magnitude of the remainder of such fields at the present epoch crucially depends on the exponent $n$ of their (initially super-Hubble) large-scale tail, i.e.
B(lambda) ~ lambda^(-n).
It has been claimed that causality requires n=5/2, contrary to much earlier claims of n=3/2.

The Evolution of the Large-Scale Tail of Primordial Magnetic Fields · Around

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The equation follows from Ref. ’s Eqs. (2.30) (with only the first term on the RHS), Eqs. (2.31), (2.33), and (2.34). The conversion of J ⁡ ( k , 0 ) J(k,0) in their Eq. (2.34) to fluid velocity may be obtained from Eqs. (3.1) and (3.4)

Cited in the paper.

One may use, for example, M ~ k ≡ M k / s 4 / 3 \tilde{M}_{k}\equiv M_{k}/s^{4/3} , provided the integral ∫ d k M k \int{\rm d}\,k\,M_{k} is performed over comoving wave vectors. Here s s is radiation entropy with s a 3 = const s\,a^{3}=\,{\rm const}

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