Viable Constraint on Scalar Field in Scalar-Tensor Theory
  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.
