As explained in the introduction, Dirac postulated that varies as the inverse of the cosmic time. Such an hypothesis is indeed not a theory since the evolution of with time is postulated and not derived from an equation of evolution12 consistent with the other field equations, that have to take into account that is no more a constant (in particular in a Lagrangian formulation one needs to take into account that is no more constant when varying.
The first implementation of Dirac’s phenomenological idea into a field-theory framework (i.e., modifying Einstein’s gravity and incorporating non-gravitational forces and matter) was proposed by Jordan . He realized that the constants have to become dynamical fields and proposed the action
Fierz  realized that with such a Lagrangian, atomic spectra will be space-time-dependent, and he proposed to fix to the value to prevent such a space-time dependence. This led to the definition of a one-parameter () class of scalar-tensor theories in which only is assumed to be a dynamical field. This was then further explored by Brans and Dicke  (with the change of notation ). In this Jordan–Fierz–Brans–Dicke theory the gravitational constant is replaced by a scalar field, which can vary both in space and time. It follows that, for cosmological solutions, with . Thus, Einstein’s gravity is recovered when . This kind of theory was further generalized to obtain various functional dependencies for in the formalisation of scalar-tensor theories of gravitation (see, e.g., Damour and Esposito-Farèse  or Will ).
Living Rev. Relativity 14, (2011), 2
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