Experimental tests of curvature couplings of fermions in general relativity

Spin-$\frac{1}{2}$ particles in geodesic trajectories experience no gravitational potential but they still have nonzero couplings to the curvature tensor. The effect of space-time curvature on fermions can be parametrized by a vector and a pseudovector potential. These apparent $\mathrm{CPT}$-violating terms can be measured with satellite-based spin-polarized torsion balance and clock comparison experiments. The Earth’s curvature effect is of the order of ${10}^{-37}\hspace{0.5em}\mathrm{GeV},$ which is not far from the present bounds of $\sim {10}^{-29}\hspace{0.5em}\mathrm{GeV}$ on such $\mathrm{CPT}$-violating couplings.