Strongly coupled chameleon fields: possible test with a neutron Lloyd's mirror interferometer

The consideration is presented of possible neutron Lloyd’s mirror interferometer experiment to search for strongly coupled chameleon fields. The chameleon scalar fields were proposed to explain the early and late time acceleration of expansion of the Universe. They may produce short-range interaction between particles and matter. This interaction causes phase shift of neutron waves in the interferometer. Estimates of sensitivity are performed.