Theoretical and experimental assessment of Einstein–Cartan theory: a comparative analysis within the USMEG-EFT framework

The Unified Standard Model with Emergent Gravity (USMEG-EFT) framework achieves Standard Model-gravity unification by treating 4D general relativity as an effective field theory (EFT). This work presents a comparative analysis of Einstein–Cartan (EC) theory and the USMEG-EFT against experimental constraints and theoretical consistency requirements, distinguishing minimal EC with algebraically determined torsion from variants in which the spin connection is an independent quantum field. The latter class includes the Faddeev–Popov quantization framework of Brandt, Frenkel, Martins-Filho, and McKeon, adopted in their unification proposal, and for which gravitational wave polarization measurements directly test the additional propagating degrees of freedom. General relativity’s spin-2 graviton produces exactly two tensor polarizations, while EC theory with independent dynamical spin connection predicts up to six modes. LIGO–Virgo–KAGRA null tests for GW170817 favor pure tensor over pure vector and pure scalar hypotheses at Bayes factors exceeding 10 20 :1, improved to approximately 10 26 :1 with a gamma-ray-burst jet-orientation prior. Complementary matter-sector constraints from the Standard Model Extension yield [Formula: see text] GeV, constraining background-torsion scenarios, while MICROSCOPE bounds equivalence principle violation at η < 1.5 × 10 −15 . For minimal EC theory, the four-fermion contact interaction generated upon coupling to fermions introduces nonrenormalizable divergence structures at two-loop order, a case not addressed by the Becchi–Rouet–Stora–Tyutin (BRST) framework established for the independent spin connection. We situate EC theory within the broader landscape of gauge gravity theories and acknowledge USMEG-EFT’s limitations, including sub-Planckian validity and currently untestable distinctive predictions. Taken together, these results render EC theory disfavored relative to USMEG-EFT as a unification framework, with distinct arguments applying to each variant: geometric extensions introducing independent torsion are neither required nor experimentally favored within currently testable parameter space.