Chameleon gravity on cosmological scales

In the conventional approach to the chameleon mechanism, by assuming a static and spherically symmetric solution in which matter density and chameleon field are given by rho= rho(r) and phi = phi(r), it has been shown that the mass of the chameleon field is matter density-dependent. In regions of high matter density such as Earth, the chameleon field is massive, in the 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. rho= rho(z), phi = phi(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 the chameleon field increases with the redshift, i. e. it is 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 the power-law potential function is in better agreement with the observational data.