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

TL;DR

This paper investigates the quantum effects of a scalar field in 2D de Sitter space with a uniform electric field, focusing on the energy-momentum tensor, trace anomaly, and effective Lagrangian, including nonminimal coupling effects.

Contribution

It provides a nonperturbative calculation of the one-loop energy-momentum tensor and effective Lagrangian for scalar QED with nonminimal coupling in 2D de Sitter space, extending previous results.

Findings

Results agree with existing literature in zero electric field case

Derived the trace anomaly for the model

Constructed the one-loop effective Lagrangian

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 Poincar\'e patch of the two-dimensional de Sitter spacetime ($\mathrm{dS_{2}}$). We also consider a direct coupling the scalar field to the Ricci scalar curvature which is parameterized 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 one-loop effective Lagrangian from the induced energy-momentum tensor.