Semiclassical Gravity Beyond General Relativity: Insights from Torsion

TL;DR

The paper addresses incorporating quantum matter effects into gravity with torsion by extending semiclassical gravity to Einstein–Cartan theory and applying Hadamard renormalization to a nonminimally coupled Klein–Gordon field. It develops a Wald-like axiomatic framework and a point-splitting renormalization scheme that yield finite, renormalized energy–momentum and spin densities, while making explicit the scale and renormalization ambiguities via a differential-form renormalization Lagrangian. It further shows that the conformal anomaly persists in the presence of torsion, with the state-dependent term $v_1$ driving the anomaly. Overall, the work demonstrates that semiclassical methods provide a robust and informative approach to exploring torsionful modifications of gravity and their potential phenomenology.

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.