Induced energy-momentum tensor in de Sitter scalar QED and its implication for induced current

The aim of this research is to investigate the vacuum energy-momentum tensor of a quantized, massive, nonminimally coupled scalar field induced by a uniform electric field background in a four-dimensional de Sitter spacetime ($\dsf$). We compute the expectation value of the energy-momentum tensor in the in-vacuum state and then regularize it using the adiabatic subtraction procedure. The correct trace anomaly of the induced energy-momentum tensor that confirmed our results is significant. The nonconservation equation for the induced energy-momentum tensor imposes the renormalization condition for the induced electric current of the scalar field. The findings of this research indicate that there are significant differences between the two induced currents which are regularized by this renormalization condition and the minimal subtraction condition.