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We have studied the induced one-loop energy-momentum tensor of a massivecomplex scalar field within the framework of nonperturbative quantumelectrodynamics (QED) with a uniform electric field background on thePoincar\'e patch of the two-dimensional de Sitter spacetime($\mathrm{dS_{2}}$). We also consider a direct coupling the scalar field to theRicci scalar curvature which is parameterized by an arbitrary dimensionlessnonminimal coupling constant. We evaluate the trace anomaly of the inducedenergy-momentum tensor. We show that our results for the inducedenergy-momentum tensor in the zero electric field case, and the trace anomalyare in agreement with the existing literature. Furthermore, we construct theone-loop effective Lagrangian from the induced energy-momentum tensor.

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