Stochastic inflationary scalar electrodynamics

We stochastically formulate the theory of scalar quantum electrodynamics on a de Sitter background. This reproduces the leading infrared logarithms at each loop order. It also allows one to sum the series of leading infrared logarithms to obtain explicit, nonperturbative results about the late time behavior of the system. One consequence is confirmation of the conjecture by Davis, Dimopoulos, Prokopec and Törnkvist that super-horizon photons acquire mass during inflation. We compute Mγ2≃3.2991×H2. The scalar stays perturbatively light with Mφ2≃0.8961×3e2H2/8π2. Interestingly, the induced change in the cosmological constant is negative, δΛ ≃ −0.6551 × 3GH4/π.