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An FLRW Cosmology with a Chameleon Field

In this manuscript, the field equations of a chameleon field in which the matter Lagrangian term is a general function of the scalar field as well as matter field, are derived. The equations are then expressed in Friedmann--Lemaître--Robertson--Walker~(FLRW) framework and the associated phase portraits and a power law solution are discussed in details. It is shown that why non-minimal coupling between the chameleon and matter fields leads to an energy transfer between the fields which consequently, affects the expansion rate of the universe. The transfer direction is determined by the second law of thermodynamics. The solution indicates that an accelerating expansion of the universe can be described as a result of the energy flow from the chameleon field to matter field.