Energy-momentum tensor and effective Lagrangian of scalar QED with a nonminimal coupling in 2D de Sitter spacetime

Abstract

We have studied the induced one-loop energy-momentum tensor of a massive complex scalar field within the framework of nonperturbative quantum electrodynamics (QED) with a uniform electric field background on the Poincaré patch of the two-dimensional de Sitter spacetime (dS₂). We also consider a direct coupling the scalar field to the Ricci scalar curvature which is parametrized by an arbitrary dimensionless nonminimal coupling constant. We evaluate the trace anomaly of the induced energy-momentum tensor. We show that our results for the induced energy-momentum tensor in the zero electric field case, and the trace anomaly are in agreement with the existing literature. Furthermore, we construct the nonperturbative, regularized, one-loop effective Lagrangian of scalar QED in dS₂ from the induced energy-momentum tensor.