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Chameleon gravity on cosmological scales

In conventional approach to the chameleon mechanism, by assuming a static and spherically symmetric solutions in which matter density and chameleon field are given by $ρ=ρ(r)$ and $ϕ=ϕ(r)$, it has been shown that mass of chameleon field is matter density-dependent. In regions of high matter density such as earth, chameleon field is massive, in solar system it is low and in cosmological scales it is very low. In this article we revisit the mechanism in cosmological scales by assuming a redshift dependence of the matter density and chameleon field, i.e. $ρ=ρ(z)$, $ϕ=ϕ(z)$. To support our analysis, we best fit the model parameters with the observational data. The result shows that in cosmological scales, the mass of chameleon field increases with the redshift, i.e. more massive in higher redshifts. We also find that in both cases of power-law and exponential potential function, the current universe acceleration can be explained by the low mass chameleon field. In comparison with the high redshift observational data, we also find that the model with power-law potential function is in better agreement with the observational data.