Kinetic approach to the Schwinger effect during inflation

Using the kinetic approach, we study the impact of the charged particle dynamics due to the Schwinger effect on the electric field evolution during inflation. As a simple model of the electric field generation, we consider the kinetic coupling of the electromagnetic field to the inflaton via the term f(2) (phi)F mu nu F mu nu with the Ratra coupling function f = exp(beta phi/M-p). The production of charged particles is taken into account in the Boltzmann kinetic equation through the Schwinger source term. Produced particles are thermalized due to collisions which we model by using the collision integral in the self-consistent relaxation time approximation. We found that the current of created particles exhibits a non-Markovian character and cannot be described by a simple Ohm's law relation j proportional to E. On the contrary, the electric current as well as the electric field are oscillatory functions of time with decreasing amplitudes and a phase difference due to the ballistic motion of charged carriers. Our qualitative results are checked by using a hydrodynamic approach. Deriving a closed system of equations for the number, current, and energy densities of charged particles and determining its solution, we find a good agreement with the results obtained in the kinetic approach.

Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis

Oleksandr Sobol

We study magnetogenesis in axionlike inflation driven by a pseudoscalar field phi coupled axially to the electromagnetic (EM) field (beta/M-p)phi F-mu nu(F) over tilde mu nu with dimensionless coupling constant beta. A set of equations for the inflaton field, scale factor, and expectation values of quadratic functions of the EM field is derived. These equations take into account the Schwinger effect and the backreaction of generated EM fields on the Universe expansion. It is found that the backreaction becomes important when the EM energy density reaches the value rho(EM) similar to (root 2 epsilon/beta)rho(inf) (epsilon is the slow-roll parameter and rho(inf) is the energy density of the inflaton) slowing down the inflaton rolling and terminating magnetogenesis. The Schwinger effect becomes relevant when the electric energy density exceeds the value rho(E) similar to alpha(-3)(EM)(rho(2)(tot)/M-p(4)), where rho(tot) = 3H(2)M(p)(2) is the total energy density and alpha(EM) is the EM coupling constant. For large beta, produced charged particles could constitute a significant part of the Universe energy density even before the preheating stage. Numerically studying magnetogenesis in the alpha-attractor model of inflation, we find that it is possible to generate helical magnetic fields with the maximal strength 10(-15) G, however, only with the correlation length of order 1 pc at present.

2019

Influence of backreaction of electric fields and Schwinger effect on inflationary magnetogenesis

Oleksandr Sobol

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. and inflaton energy density,rho(E) similar to epsilon rho(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) G. It is worth emphasizing that since the effective electric charge of particles e(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 proportional to a(a) and Ratra-type f = expo(beta phi/M-p) coupling functions.

2018

Schwinger production of scalar particles during and after inflation from the first principles

Oleksandr Sobol

By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet asymptotic behavior of the kinetic functions, we found the divergent parts of the electric current and the energy-momentum tensor of the produced particles and determined the corresponding counterterms. The renormalized system of equations is used to study the generation of electromagnetic fields during and after inflation in the kinetic coupling model L-EM = -(1/4)f(2)(phi)F-mu nu F-mu nu with the Ratra coupling function f = exp(beta phi/M-p). It is found that the electric current of created particles is retarded with respect to the electric field. This leads to an oscillatory behavior of both quantities in agreement with the results obtained previously in phenomenological kinetic and hydrodynamical approaches.

2020