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The viability of slow-roll approximation is examined by considering thestructure of phase spaces in scalar-tensor theories of gravitation and theanalysis is exemplified with a nonminimally coupled scalar field to thespacetime curvature. The slow-roll field equations are obtained in the Jordanframe in two ways: first using the direct generalization of the slow-rollconditions in the minimal coupling case to nonminimal one, and second,conformal transforming the slow-roll field equations in the Einstein frame tothe Jordan frame and then applying the generalized slow-roll conditions. Twoinflationary models governed by the potentials $V(\phi) \propto \phi^2$ and$V(\phi) \propto \phi^4$ are considered to compare the outcomes of two methodsbased on the analysis of $n_s$ and $r$ values in the light of recentobservational data.

Formalizing Slow-roll Inflation in Scalar-Tensor Theories of Gravitation