We analyze a possibility to probe beyond-Riemann gravity (BRG) contributions, introduced by Kostelecký and Li (see Kostelecký and Li (2021) [6]) on the basis of the Effective Field Theory (EFT) by Kostelecký (2004) [4]. 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 Kostelecký and Li (2021) [6].
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