Dynamics of a spinning test body in a Poincaré gauge theory of gravity and its free-fall test

We study the dynamics of the nonrelativistic spinning test body (STB) in the framework of Poincar\'e gauge theory of gravity (PGT), in which the weak equivalence principle is violated by the spin-gravitational interaction. We derive the general geodesic equation in terms of comoving tetrads. More concretely, we consider the case of the quadratic form of the Lagrangian, within the environment of a weak and static spherically symmetric space-time. We find that the trajectories of a STB deviate from the traditional Mathisson-Papapetrou equation, which is due to the coupling of the spin of the test particle to the torsion field of the environment. This allows us to test the theory with a free-fall experiment in the laboratory, such as with an atom interferometer. By using the previous data, we find the upper bound of the possible torsion field on Earth is given by up to $2.0\ifmmode\times\else\texttimes\fi{}{10}^{1}\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}1}$ and torsion gradient up to $3.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}2}$. This result may enable us to provide a theoretical foundation for future precision measurements of the existence of the fifth force.

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