The present work is an extensive study of the viable stable solutions of chameleon scalar field models leading to possibilities of an accelerated expansion of the universe. It is found that for various combinations of the chameleon field potential V(phi) and the coupling f (phi) of the chameleon field with matter, a stable solution for an accelerated expansion is quite possible. The investigation provides a diagnostics for the stability criteria for all sorts of combinations of V(phi) and f (phi). (C) 2015 Elsevier Inc. All rights reserved.
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