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
evolution^{12}
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

and being two parameters. It follows that both and the fine-structure constant have been promoted to the status of a dynamical field.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]).

5.1 Introducing new fields: generalities

5.1.1 The example of scalar-tensor theories

5.1.2 Making other constants dynamical

5.2 High-energy theories and varying constants

5.2.1 Kaluza–Klein

5.2.2 String theory

5.3 Relations between constants

5.3.1 Implication of gauge coupling unification

5.3.2 Masses and binding energies

5.3.3 Gyromagnetic factors

5.4 Models with varying constants

5.4.1 String dilaton and Runaway dilaton models

5.4.2 The Chameleon mechanism

5.4.3 Bekenstein and related models

5.4.4 Other ideas

5.1.1 The example of scalar-tensor theories

5.1.2 Making other constants dynamical

5.2 High-energy theories and varying constants

5.2.1 Kaluza–Klein

5.2.2 String theory

5.3 Relations between constants

5.3.1 Implication of gauge coupling unification

5.3.2 Masses and binding energies

5.3.3 Gyromagnetic factors

5.4 Models with varying constants

5.4.1 String dilaton and Runaway dilaton models

5.4.2 The Chameleon mechanism

5.4.3 Bekenstein and related models

5.4.4 Other ideas

Living Rev. Relativity 14, (2011), 2
http://www.livingreviews.org/lrr-2011-2 |
This work is licensed under a Creative Commons License. E-mail us: |