  Among the known particles, the neutron takes a special position, as it
provides experimental access to all four fundamental forces and a wide range of
hypothetical interactions. Despite being unstable, free neutrons live long
enough to be used as test particles in interferometric, spectroscopic, and
scattering experiments probing low-energy scales. As was already recognized in
the 1970s, fundamental concepts of quantum mechanics can be tested in neutron
interferometry using silicon perfect-single-crystals. Besides allowing for
tests of uncertainty relations, Bell inequalities and alike, neutrons offer the
opportunity to observe the effects of gravity and hypothetical dark forces
acting on extended matter wave functions. Such tests gain importance in the
light of recent discoveries of inconsistencies in our understanding of
cosmology as well as the incompatibility between quantum mechanics and general
relativity. Experiments with low-energy neutrons are thus indispensable tools
for probing fundamental physics and represent a complementary approach to
colliders. In this review we discuss the history and experimental methods used
at this low-energy frontier of physics and collect bounds and limits on quantum
mechanical relations and dark energy interactions.
