Constraints on spin-dependent short-range interactions using gravitational quantum levels of ultracold neutrons

In this paper, we discuss a possibility to improve constraints on spin-dependent short-range interactions in the range of 1 - 200 micrometer significantly. For such interactions, our constraints are without competition at the moment. They were obtained through the observation of gravitationally bound states of ultracold neutrons. We are going to improve these constraints by about three orders of magnitude in a dedicated experiment with polarized neutrons using the next-generation spectrometer GRANIT.