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 [268]. He realized that the constants have to become dynamical fields and proposed the action
Fierz [195] 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 [67] (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 [124
] or
Will [540]).
http://www.livingreviews.org/lrr-2011-2 |
Living Rev. Relativity 14, (2011), 2
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