Self-similar chameleon Jordan-Brans-Dicke cosmological models

In this paper we study the chameleon Jordan-Brans-Dicke (JBD) cosmological models under the hypothesis of self-similarity. Since there are several ways to define the matter Lagrangian for a perfect fluid: L _m =?ρ and L _m =γρ, we show that they bring us to obtain two completely different cosmological models. In the first approach, L _m =?ρ, there is ordinary matter conservation, while in the second approach, L _m =γρ, we get matter creation processes. We deduce for each approach the behaviour of each physical quantity, under the self-similar hypothesis, by employing the Lie group method. The results are quite general and valid for any homogeneous geometry (FRW, Bianchi types, etc.). As example, we calculate exact solutions for each approach by considering the case of a Bianchi II geometry. In this way we can determine the exact behaviour of each physical quantity and in particular of G _eff and U (the potential that mimics the cosmological constant).We compare the solutions with the obtained ones in the framework of the usual JBD models.