Flattening of the axion potential and vacuum energy

Starting with a cosine bare potential, we argue that, if no other particle interacts with the axion, the quantized theory should be described by a flat potential. This feature therefore restores the would-be Goldstone-boson nature of the axion, and we calculate the corresponding vacuum energy density. We discuss then the role of interactions with other particles, which can prevent the cosine potential from flattening