Role of Chameleon Field in presence of Variable Modified Chaplygin gas in Brans-Dicke Theory

In this work, we have considered the Friedmann–Robertson–Walker model of the universe for Brans–Dicke (BD) theory with a BD scalar field as a chameleon field. First we have transformed the field equations and conservation equation from Jordan’s frame to Einstein’s frame. We have shown that, in the presence of a variable modified Chaplygin gas (VMCG), the potential function V and another analytic function f always increase with respect to the BD–chameleon scalar field [Formula: see text] but decrease with time t for pure Chaplygin gas, modified Chaplygin gas, and VMCG models.