Schwinger Pair Creation by a Time-Dependent Electric Field in de Sitter Space with the Energy Density E_μ E^μ=E^2 a^2(τ)

We investigate Schwinger pair creation of charged scalar particles from a time-dependent electric field background in (1+3)-dimensional de Sitter spacetime. Since the field’s equation of motion has no exact analytical solution, we employ Olver’s uniform asymptotic approximation method to find its analytical approximate solutions. Depending on the value of the electric field E, and the particle’s mass m, and wave vector k, the equation of motion has two turning points, whose different natures (real, complex, or double) lead to different pair production probability. More precisely, we find that for the turning points to be real and single, m and k should be small, and the more smaller are the easier to create the particles. On the other hand, when m or k is large enough, both turning points are complex, and the pair creation is exponentially suppressed. In addition, we study the pair creation in the weak electric field limit, and find that the semi-classical electric current responds as E