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

Abstract

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. This work presents a comparative analysis of Einstein-Cartan (EC) theory and 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 it 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 $|{\tilde{b}}_{\perp }^n|<8.4\times 10^{-34}$ GeV, constraining background-torsion scenarios, while MICROSCOPE bounds equivalence principle violation at $\eta <1.5\times 10^{-15}$. For minimal EC theory, the four-fermion contact interaction generated upon coupling to fermions introduces non-renormalizable divergence structures at two-loop order, a case not addressed by the 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.

arXiv comment14 pages, published at Canadian Journal of Physics