  We analyze a possibility to probe beyond-Riemann gravity (BRG) contributions,
introduced by Kostelecky and Li (see Phys. Rev. D 103, 024059 (2021) and Phys.
Rev. D 104, 044054 (2021)) on the basis of the Effective Field Theory (EFT) by
Kostelecky Phys. Rev. D 69, 105009 (2004). We carry out such an analysis by
calculating the BRG contributions to the transition frequencies of the quantum
gravitational states of ultracold neutrons (UCNs). These states are being used
for a test of interactions beyond the Standard Model (SM) and General
Relativity (GR) in the qBOUNCE experiments. We improve by order of magnitude
some constraints obtained by Kostelecky and Li (2106.11293 [gr-qc]).
