Sobol O. Gauge field production at the stage of cosmological inflation

This thesis (scientific report) is devoted to a theoretical study of the generation of Abelian gauge fields at the stage of inflation in the early Universe and various phenomenological aspects of this scenario: the backreaction of the generated fields, the production of charged particles due to the Schwinger effect, the generation of fermionic chiral asymmetry, the formation of primordial scalar perturbations etc. In the first section, we consider the interaction of the gauge field with the inflaton scalar field in the kinetic coupling model. The generation of individual Fourier modes of gauge fields in momentum space is described in the linear evolution regime. We propose a new method for the description of the gauge field generation, the gradient expansion formalism, which allows us to take into account such nonlinear phenomena as the backreaction of the generated fields to inflationary dynamics and the Schwinger production of pairs of charged particles in a self-consistent manner. This method was used to determine the peculiarities of the strong backreaction regime in the kinetic coupling model: The energy density of the generated fields stops growing abruptly and exhibits oscillatory behavior, the inflationary phase lengthens, and the inflaton field slows down its rolling and smoothly slides to the minimum of its potential. The second section is devoted to magnetogenesis in the model of axial coupling between the gauge field and the inflaton. Using the gradient expansion formalism, we obtain model-independent estimates for the magnitude of gauge fields generated in the axion inflation model. In the strong backreaction regime, it is shown that the Anber-Sorbo solution, in which energy losses due to the gauge field production provide the dominant source of friction during the rolling of the inflaton, is not stable in any region of parameters and initial conditions. We calculate the current value of the magnetic field in voids that can be generated in the axial coupling model. In the third section, we analyze the possibilities of generating gauge fields in models with a nonminimal coupling to gravity. In the Higgs and Higgs-Starobinsky inflation models, explicit expressions for the kinetic and axial coupling functions in the Einstein frame are obtained. The generation of gauge fields in the linear regime in the absence of backreaction is described. The modified Starobinsky model can potentially generate gauge fields with a spectrum that is scale-invariant or even red-tilted. However, the backreaction that inevitably occurs in this model strongly changes the behavior of the spectrum and does not allow for a sufficiently large correlation length of the magnetic field. In the fourth section, we study the peculiarities of the Schwinger pair-production of charged particles and antiparticles in strong gauge fields during inflation. In the approximation where the current of the produced particles is described by the generalized Ohm’s law, we apply the gradient expansion formalism and show that the Schwinger effect strongly suppresses the generation of gauge fields, so that their backreaction is always negligible. A system of quantum kinetic equations describing the production of scalar particles by a strong electric field in the early Universe is derived from first principles. Using kinetic and hydrodynamic approaches, the dynamics of Schwinger particle production in a strong electric field is considered and the nonlocal character of the induced current of the produced particles is revealed, which is related to the inertial properties of charge carriers. The fifth section is devoted to the description of the generation and equilibration of the chiral asymmetry of fermions in the early Universe. In particular, it is found that in helical gauge fields the asymmetry generated by the chiral anomaly can be up to 25 % of the total fermion number density. Using the Boltzmann kinetic equation and the linear response formalism, we calculate the rate of equilibration of the chiral asymmetry due to the presence of nonzero particles’ mass. It is shown that the rate of reactions with chirality flipping is nonzero already in the first order in the fine structure constant, and therefore its numerical value in the early Universe is about three orders of magnitude larger than expected from naive estimates. In the sixth section, the generation of primordial scalar perturbations during inflation in the presence of gauge fields is studied. A differential equation for the curvature perturbation is derived, which takes into account the influence of the gauge field on both the background dynamics and the evolution of scalar perturbations through the source term which is quadratic in the gauge field operators and leads to non-Gaussianity of the curvature perturbations. The general expressions for the spectra of two- and three-point correlation functions of the primordial perturbations are obtained.