The viability of slow-roll approximation is examined by considering the structure of phase spaces in scalar–tensor theories of gravitation and the analysis is exemplified with a nonminimally coupled scalar field to the spacetime curvature. The slow-roll field equations are obtained in the Jordan frame in two ways: first using the direct generalization of the slow-roll conditions in the minimal coupling case to nonminimal one, and second, conformal transforming the slow-roll field equations in the Einstein frame to the Jordan frame and then applying the generalized slow-roll conditions. Two inflationary models governed by the potentials $V\left(\varphi \right)\propto {\varphi }^2$ and $V\left(\varphi \right)\propto {\varphi }^4$ are considered to compare the outcomes of two methods based on the analysis of $n_s$ and $r$ values in the light of recent observational data.

通过考虑标量-张量引力理论中相空间的结构来检验慢滚动逼近的可行性，并以非最小耦合标量场与时空曲率的分析为例进行分析。在Jordan框架中以两种方式获得慢滚场方程：首先，将最小耦合情况下的慢滚条件直接推广到非最小的情况；其次，将爱因斯坦中的慢滚场方程进行保形变换帧到Jordan帧，然后应用广义的慢摇条件。由潜力控制的两种通货膨胀模型$V（\varphi ）\propto {\varphi }^2$ 和 $V（\varphi ）\propto {\varphi }^4$ 被认为是比较两种方法的结果的基础上的分析 ${ñ}_s$ 和 $\mathrm{[R}$ 根据最近的观测数据得出的数值。