The scalar-tensor theory can be formulated in both Jordan and Einstein frames, which are conformally related together with a redefinition of the scalar field. As the solution to the equation of the scalar field in the Jordan frame does not have the one-to-one correspondence with that in the Einstein frame, we give a criterion along with some specific models to check if the scalar field in the Einstein frame is viable or not by confirming whether this field is reversible back to the Jordan frame. We further show that the criterion in the first parameterized post-Newtonian approximation can be determined by the parameters of the osculating approximation of the coupling function in the Einstein frame and can be treated as a viable constraint on any numerical study in the scalar-tensor scenario. We also demonstrate that the Brans-Dicke theory with an infinite constant parameter $\omega_{\text{BD}}$ is a counterexample of the equivalence between two conformal frames due to the violation of the viable constraint.

中文翻译：

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标量张量理论中标量场的可行约束

标量张量理论可以在 Jordan 和 Einstein 框架中表述，它们与标量场的重新定义共形相关。由于乔丹坐标系中标量场方程的解与爱因斯坦坐标系中的解不存在一一对应关系，我们给出一个判据以及一些具体的模型来检验爱因斯坦坐标系中的标量场方程是否存在通过确认该场是否可逆回到乔丹框架来确定是否可行。我们进一步表明，第一个参数化后牛顿近似中的准则可以由爱因斯坦坐标系中耦合函数的密切近似的参数确定，并且可以被视为对标量张量场景中任何数值研究的可行约束.