Semiclassical Gravity Beyond General Relativity: Insights from Torsion

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.