We investigate hidden symmetries in minimally coupled scalar field cosmology within the FLRW universe, and a perfect fluid with and without interaction to the scalar field. We show that for an exponential potential there exists a set of canonical transformations through which the cosmological field equations can be recast in the form of a free particle in flat space. Based on this equivalence, we construct a mapping that generates cosmological solutions with interaction terms, corresponding to a chameleon mechanism. Finally, we discuss how this class of canonical transformations can relate the solution spaces of different cosmological models, such as of the scalar field and of the -Cosmology.
Andronikos Paliathanasis (Wed,) studied this question.