Covarying Coupling Constants and Tired Light-like Hypotheses from the Covarying-Bi-Scalar Theory

This paper presents an attempt to provide a scalar-tensor theoretical foundation for the Covarying Coupling Constants plus Tired Light-like (CCC+TL) phenomenological framework. This is done in the context of the Covarying-Bi-Scalar Theory (CBST) in which the gravitational coupling G and the speed of light c vary simultaneously while respecting a constraint of the type G∝c3. This constraint is a global stable critical point of their dynamical evolution in the early universe. In a previous work, it was shown that the varying couplings give rise to a screening mechanism in the Jordan frame, dubbed the c-meleon mechanism. Here, we reconstruct the potential Vφ for the c-meleon field φ∝lnc/c0, thereby explaining the CCC hypothesis used by one of the authors with phenomenological success. The TL-like behavior of the field φ is obtained from the spatial dependence of the perturbation of φ on top of an FLRW background. This work is a step towards a fundamental justification for CCC+TL based on a scalar-tensor theory for modified gravity in the context of our CBST framework.