Large-scale magnetic fields, curvature fluctuations, and the thermal history of the Universe

It is shown that gravitating magnetic fields affect the evolution of curvature perturbations in a way that is reminiscent of a pristine nonadiabatic pressure fluctuation. The gauge-invariant evolution of curvature perturbations is used to constrain the magnetic power spectrum. Depending on the essential features of the thermodynamic history of the Universe, the explicit derivation of the bound is modified. The theoretical uncertainty in the constraints on the magnetic energy spectrum is assessed by comparing the results obtained in the case of the conventional thermal history with the estimates stemming from less conventional (but phenomenologically allowed) post-inflationary evolutions.

Figure 1

The bounds on the smoothed magnetic field intensity are illustrated as a function of the magnetic spectral index (plot at the left) and as a function of the critical fraction in dusty matter (plot at the right). The pivot scales $k_{\mathrm{p}}$ and $k_{\mathrm{L}}$ are fixed, respectively, to $0.002{\mathrm{Mpc}}^{-1}$ and ${\mathrm{Mpc}}^{-1}$.

Figure 2

The bounds on the smoothed magnetic field intensity are illustrated as a function of the correlation angle $\gamma$ (plot at the left) and as a function of the adiabatic spectral index $n_{\zeta }$ (plot at the right). All the other parameters are kept fixed to their fiducial values.

Figure 3

The potential differences in the estimate of the diffusion scale are illustrated. In the plot at the left, the bunch of curves labeled by B corresponds to the estimate of the diffusion scale given in Eq. (4.12) while the curves labeled by A are the same illustrated in Fig. 1 (plot at the left). In the plot at the right the two classes of curves have illustrated the same phenomenon but in terms of the dependence on $n_{\zeta }$ and should be compared with the right plot appearing in Fig. 2.