http://arxiv.org/abs/1807.09851
We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell’s action is broken by the kinetic coupling $f^{2}(\phi)F_{\mu\nu}F^{\mu\nu}$ of the electromagnetic field to the inflaton field $\phi$. We consider the case where the coupling function $f(\phi)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The back-reaction of electric fields is relevant for inflationary magnetogenesis for a certain range of parameters, where it affects the inflaton field evolution and leads to the scale invariant electric power spectrum and the magnetic one which is blue with the spectral index $n_{B}=2$ for any decreasing coupling function. Unfortunately, this gives an upper limit on the present day value of large-scale magnetic fields below $10^{-22}\,{\rm G}$. It is worth emphasizing that since the effective electric charge of particles $e_{\rm eff}=e/f$ is suppressed by the coupling function, the Schwinger effect becomes important only at the late stages of inflation when the inflaton field is close to the minimum of its potential. The Schwinger effect abruptly decreases the value of the electric field helping to finish the inflation stage and enter the stage of preheating. It effectively produces the charged particles implementing the Schwinger reheating scenario even before the fast oscillations of the inflaton.
O. Sobol, E. Gorbar, M. Kamarpour, et. al.
Mon, 6 Aug 18
29/33
Comments: 20 pages, 6 figures. Comments are welcome
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