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.
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