Potential of the neutron Lloyd's mirror interferometer for the search for new interactions

We discuss the potential of the neutron Lloyd's mirror interferometer in a search for new interactions at small scales. We consider three hypothetical interactions that may be tested using the interferometer. The chameleon scalar field proposed to solve the enigma of accelerating expansion of the Universe produces interaction between particles and matter. The axion-like spin-dependent coupling between neutron and nuclei or/and electrons may cause P- and T-non-invariant interaction with matter. Hypothetical non-Newtonian gravitational interactions mediates additional short-range potential between neutrons and bulk matter. These interactions between the neutron and the mirror of the Lloyd's type neutron interferometer cause phase shift of neutron waves. We estimate the sensitivity and systematic effects of possible experiments.