This work presents selected results from the first round of the DFG Priority Programme SPP 1491 precision experiments in particle and astroparticle physics with cold and ultra-cold neutrons.
We present two new types of spectroscopy methods for cold and ultra-cold neutrons. The first method, which uses the RB drift effect to disperse charged particles in a uniformly curved magnetic field, allows to study neutron $beta$-decay. We aim for a
precision on the 10$^{-4}$ level. The second method that we refer to as gravity resonance spectroscopy (GRS) allows to test Newtons gravity law at short distances. At the level of precision we are able to provide constraints on any possible gravity-like interaction. In particular, limits on dark energy chameleon fields are improved by several orders of magnitude.
