Trace of energy-momentum tensor and gravitational backreaction of Schwinger scalars in 3D de Sitter spacetime

In this paper, we consider a massive charged scalar field coupled to a uniform electric field background in a 3 dimensional de Sitter spacetime. We consider the value of the dimensionless coupling constant of the scalar field to the scalar curvature of a 3 dimensional de Sitter spacetime equal to 1/8. We compute the expectation value of the trace of the energy-momentum tensor in the in-vacuum state and we show that using adiabatic subtraction regularization method the linear ultraviolet divergence is removed and a finite expression obtain. We investigate the behavior of the regularized trace for different intensities of the scalar field mass and the electric field. We show that the trace as a function of the electric field has a discontinuity at which it changes the sign. We show that for the case of a conformally coupled scalar field to the de Sitter spacetime the trace vanishes, and there is no trace anomaly. We discuss the gravitational backreaction effect of the created Schwinger pairs.