Viable Constraint on Scalar Field in Scalar-Tensor Theory

Abstract

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.

18 pages, 2 figures, accepted for publication in Classical and Quantum Gravity

References in corpus (6)

• The Confrontation between General Relativity and Experiment
• The (pseudo)issue of the conformal frame revisited
• Physical non-equivalence of the Jordan and Einstein frames
• Long-lived inverse chirp signals from core collapse in massive scalar-tensor gravity
• Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frame
• Parametrizations in scalar-tensor theories of gravity and the limit of general relativity

Cited by in corpus (2)

• Core collapse in massive scalar-tensor gravity
• Inverse-Chirp Imprint of Gravitational Wave Signals in Scalar Tensor Theory