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We derive the equations of motion in metric-affine gravity by making use ofthe conservation laws obtained from Noether's theorem. The results are given inthe form of propagation equations for the multipole decomposition of the mattersources in metric-affine gravity, i.e., the canonical energy-momentum currentand the hypermomentum current. In particular, the propagation equations allowfor a derivation of the equations of motion of test particles in thisgeneralized gravity theory, and allow for direct identification of thecouplings between the matter currents and the gauge gravitational fieldstrengths of the theory, namely, the curvature, the torsion, and thenonmetricity. We demonstrate that the possible non-Riemannian spacetimegeometry can only be detected with the help of the test bodies that are formedof matter with microstructure. Ordinary gravitating matter, i.e., matterwithout microscopic internal degrees of freedom, can probe only the Riemannianspacetime geometry. Thereby, we generalize previous results of generalrelativity and Poincare gauge theory.

Propagation equations for deformable test bodies with microstructure in extended theories of gravity