Abstract
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 backreaction occurs when the electric energy density becomes as large as the product of the slow-roll parameter $\epsilon$ and inflaton energy density, $\rho_{E}\sim \epsilon \rho_{\rm inf}$. 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. This gives an upper limit on the present-day value of observed 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. The numerical analysis is carried out in the Starobinsky model of inflation for the powerlike $f\propto a^{\alpha}$ and Ratra-type $f=\exp(\beta\phi/M_{p})$ coupling functions.
Highlights
One of the important problems of modern cosmology is the origin of the magnetic fields which are present at all scales in the Universe [1,2,3,4,5,6,7,8], especially of the magnetic fields detected in the cosmic voids through the gamma-ray observations of distant blazars [9,10,11,12,13] with very large coherence scale λB ≳ 1 Mpc
We have studied how the backreaction of electric fields and the Schwinger effect influence the inflationary magnetogenesis in the model with the standard kinetic coupling of the electromagnetic field to the inflaton f2ðφÞFμνFμν and decreasing coupling function fðφÞ
Such a model leads to the generation of strong electric fields which dominate over the magnetic ones and backreact on the inflationary dynamics
Summary
One of the important problems of modern cosmology is the origin of the magnetic fields which are present at all scales in the Universe [1,2,3,4,5,6,7,8], especially of the magnetic fields detected in the cosmic voids through the gamma-ray observations of distant blazars [9,10,11,12,13] with very large coherence scale λB ≳ 1 Mpc. The cosmological Schwinger effect relates the particle production by an electric field and the exponential expansion of the Universe and contains interesting features which are absent in its flat-space counterpart, namely (i) the infrared hyperconductivity in the bosonic case when the conductivity becomes very large in the limit of small mass of charged particles and (ii) the negative conductivity in the weak-field regime eE ≪ H2 which can, in principle, lead to the enhancement of the electric field. We derive a selfconsistent system of equations which describes the joint evolution of the scale factor, inflaton field, and electric field energy density in Sec. II, where we take into account the backreaction of generated fields on the background evolution and the Schwinger effect which is important at the late stages of inflation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
