Primordial magnetic fields and nonlinear electrodynamics

The creation of large scale magnetic fields is studied in an inflationary universe where electrodynamics is assumed to be nonlinear. After inflation ends electrodynamics becomes linear and thus the description of reheating and the subsequent radiation dominated stage are unaltered. The nonlinear regime of electrodynamics is described by Lagrangians having a power-law dependence on one of the invariants of the electromagnetic field. It is found that there is a range of parameters for which primordial magnetic fields of cosmologically interesting strengths can be created.

Figure 1

For $\lambda =1\mathrm{Mpc}$ $\log r$ [cf. Eq. (3.21)] is shown as a function of $\delta$ for $T_{RH}={10}^{17}\mathrm{GeV}$ (black line) and $T_{RH}={10}^9\mathrm{GeV}$ (long-dashed line). The dashed line corresponds to $r={10}^{-37}$.

Figure 2

For $\lambda =1\mathrm{Mpc}$ $\log r$ [cf. Eq. (3.44)] is shown as a function of $\delta$ for $T_{RH}={10}^{17}\mathrm{GeV}$ (black line) and $T_{RH}={10}^9\mathrm{GeV}$ (long-dashed line). The dashed line corresponds to $r={10}^{-37}$. The left panel corresponds to the case ${\overrightarrow{P}}_k^2>0$. The right panel corresponds to the case ${\overrightarrow{P}}_k^2=0$.