  There is a deep connection between cosmology -- the science of the infinitely
large --and particle physics -- the science of the infinitely small. This
connection is particularly manifest in neutron particle physics. Basic
properties of the neutron -- its Electric Dipole Moment and its lifetime -- are
intertwined with baryogenesis and nucleosynthesis in the early Universe. I will
cover this topic in the first part, that will also serve as an introduction (or
rather a quick recap) of neutron physics and Big Bang cosmology. Then, the rest
of the manuscript will be devoted to a new idea: using neutrons to probe models
of Dark Energy. In the second part, I will present the chameleon theory: a
light scalar field accounting for the late accelerated expansion of the
Universe, which interacts with matter in such a way that it does not mediate a
fifth force between macroscopic bodies. However, neutrons can alleviate the
chameleon mechanism and reveal the presence of the scalar field with properly
designed experiments. In the third part, I will describe a recent experiment
performed with a neutron interferometer at the Institut Laue Langevin that sets
already interesting constraints on the chameleon theory. Last, the chameleon
field can be probed by measuring the quantum states of neutrons bouncing over a
mirror. In the fourth part I will present the status and prospects of the
GRANIT experiment at the ILL.
