This section focuses on the experimental and observational constraints on the non-gravitational constants, that is assuming remains constant. We use the convention that for any constant , so that refers to a value smaller than today.

The various physical systems that have been considered can be classified in many ways. We can classify them according to their look-back time and more precisely their space-time position relative to our actual position. This is summarized in Figure 1. Indeed higher redshift systems offer the possibility to set constraints on a larger time scale, but this is at the expense of usually involving other parameters such as the cosmological parameters. This is, in particular, the case of the cosmic microwave background or of primordial nucleosynthesis. The systems can also be classified in terms of the physics they involve. For instance, atomics clocks, quasar absorption spectra and the cosmic microwave background require only to use quantum electrodynamics to draw the primary constraints while the Oklo phenomenon, meteorites dating and nucleosynthesis require nuclear physics.

For any system, setting constraints goes through several steps. First we have some observable quantities from which we can draw constraints on primary constants, which may not be fundamental constants (e.g., the BBN parameters, the lifetime of -decayers, …). These primary parameters must then be related to some fundamental constants such as masses and couplings. In a last step, the number of constants can be reduced by relating them in some unification schemes. Indeed each step requires a specific modelization and hypothesis and has its own limitations. This is summarized on Table 5.

System | Observable | Primary constraints | Other hypothesis |

Atomic clock | – | ||

Oklo phenomenon | isotopic ratio | geophysical model | |

Meteorite dating | isotopic ratio | – | |

Quasar spectra | atomic spectra | cloud physical properties | |

Stellar physics | element abundances | stellar model | |

21 cm | cosmological model | ||

CMB | cosmological model | ||

BBN | light element abundances | cosmological model | |

3.1 Atomic clocks

3.1.1 Atomic spectra and constants

3.1.2 Experimental constraints

3.1.3 Physical interpretation

3.1.4 Future evolutions

3.2 The Oklo phenomenon

3.2.1 A natural nuclear reactor

3.2.2 Constraining the shift of the resonance energy

3.2.3 From the resonance energy to fundamental constants

3.3 Meteorite dating

3.3.1 Long lived -decays

3.3.2 Long lived -decays

3.3.3 Conclusions

3.4 Quasar absorption spectra

3.4.1 Generalities

3.4.2 Alkali doublet method (AD)

3.4.3 Many multiplet method (MM)

3.4.4 Single ion differential measurement (SIDAM)

3.4.5 H i-21 cm vs. UV:

3.4.6 H i vs. molecular transitions:

3.4.7 OH - 18 cm:

3.4.8 Far infrared fine-structure lines:

3.4.9 “Conjugate” satellite OH lines:

3.4.10 Molecular spectra and the electron-to-proton mass ratio

Constraints with H_{2}

Other constraints

New possibilities

3.4.11 Emission spectra

3.4.12 Conclusion and prospects

3.5 Stellar constraints

3.6 Cosmic Microwave Background

3.7 21 cm

3.8 Big bang nucleosynthesis

3.8.1 Overview

3.8.2 Constants everywhere…

3.8.3 From BBN parameters to fundamental constants

3.8.4 Conclusion

3.1.1 Atomic spectra and constants

3.1.2 Experimental constraints

3.1.3 Physical interpretation

3.1.4 Future evolutions

3.2 The Oklo phenomenon

3.2.1 A natural nuclear reactor

3.2.2 Constraining the shift of the resonance energy

3.2.3 From the resonance energy to fundamental constants

3.3 Meteorite dating

3.3.1 Long lived -decays

3.3.2 Long lived -decays

3.3.3 Conclusions

3.4 Quasar absorption spectra

3.4.1 Generalities

3.4.2 Alkali doublet method (AD)

3.4.3 Many multiplet method (MM)

3.4.4 Single ion differential measurement (SIDAM)

3.4.5 H i-21 cm vs. UV:

3.4.6 H i vs. molecular transitions:

3.4.7 OH - 18 cm:

3.4.8 Far infrared fine-structure lines:

3.4.9 “Conjugate” satellite OH lines:

3.4.10 Molecular spectra and the electron-to-proton mass ratio

Constraints with H

Other constraints

New possibilities

3.4.11 Emission spectra

3.4.12 Conclusion and prospects

3.5 Stellar constraints

3.6 Cosmic Microwave Background

3.7 21 cm

3.8 Big bang nucleosynthesis

3.8.1 Overview

3.8.2 Constants everywhere…

3.8.3 From BBN parameters to fundamental constants

3.8.4 Conclusion

Living Rev. Relativity 14, (2011), 2
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