Induced energy-momentum tensor of the scalar field in 3D de Sitter QED

TL;DR

This paper calculates the finite, renormalized energy-momentum tensor for a charged scalar field in 3D de Sitter space with an electric field, revealing its behavior across different regimes and confirming the absence of a Weyl anomaly in odd dimensions.

Contribution

It provides explicit finite expressions for the energy-momentum tensor using adiabatic regularization and analyzes its physical behavior in various parameter regimes.

Findings

Energy density grows quadratically with field strength.

Tensor components show inverse-mass dependence in infrared.

Trace anomaly vanishes for massless, conformally coupled scalar.

Abstract

In this work, we investigate the renormalized energy--momentum tensor of a quantized charged scalar field in three-dimensional de Sitter spacetime $\mathrm{dS}_{3}$ under the influence of a uniform electric field. Using the adiabatic regularization method, we systematically remove ultraviolet divergences and obtain explicit finite expressions for the components of the induced energy--momentum tensor. The numerical analysis demonstrates that the renormalized tensor behaves smoothly with respect to the parameters of the system and exhibits physically consistent limits in both the strong-field and infrared regimes. The induced energy density grows with the field strength and follows a quadratic behavior, which is consistent with the Schwinger mechanism in three dimension. In the opposite infrared regime, the tensor components display inverse-mass dependence, revealing infrared divergences typical of nearly massless scalar fields in curved space. Finally, we evaluate the trace of the renormalized tensor and show that for a massless, conformally coupled scalar field the trace anomaly vanishes, confirming the absence of a genuine Weyl anomaly in odd-dimensional spacetimes. These results provide a consistent and covariant description of quantum vacuum polarization and backreaction effects in three-dimensional de Sitter geometry.