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In this work, we derive the analytical form for a $f(R)$ model that describesa perfect scalar field $\phi$ by assuming the existence of a chameleonmechanism. Based on four statements, at the background and perturbative level,it is possible to relate the extra terms from this theory as a geometricalperfect fluid term, whose has been expressed as possible candidates to explainthe nature of the dark sector, and possibly, in the case of a perfect scalarchameleon during inflation, satisfy the big bang nucleosynthesis (BBN)constraints until late times.

Chameleon perfect scalar field as a geometric correction in $f(R)$ gravity