Semiclassical Gravity Beyond General Relativity: Insights from Torsion

TL;DR

This paper develops a semiclassical theory of modified gravity incorporating spacetime torsion, providing a framework for renormalized energy-momentum and spin-density expectations, and analyzing the conformal anomaly within Einstein--Cartan theory.

Contribution

It introduces a semiclassical approach to Einstein--Cartan theory with nonminimally coupled fields, including renormalization techniques and anomaly analysis.

Findings

Renormalized expectation values for energy--momentum and spin--density are well-defined.

Identified renormalization ambiguities and constructed a differential forms-based Lagrangian.

Analyzed the persistence of the conformal anomaly in torsion-inclusive gravity.

Abstract

We develop a semiclassical theory of modified gravity with nontrivial spacetime torsion. In particular, we show that the semiclassical treatment can be axiomatized in the case of Einstein--Cartan theory with a nonminimally coupled, free Klein--Gordon field, in four dimensions. Using Hadamard renormalization, we obtain well-defined expectation values for both, the energy--momentum and spin--density operators. These objects exhibit scale and renormalization ambiguities; we identify the latter by constructing a renormalization Lagrangian in terms of differential forms, which are particularly well suited for this purpose. Furthermore, we analyze the conformal anomaly, which persists in the presence of torsion.