3 Experimental and Observational Constraints

This section focuses on the experimental and observational constraints on the non-gravitational constants, that is assuming α G remains constant. We use the convention that Δ α = α − α 0 for any constant α, so that Δ α < 0 refers to a value smaller than today.

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Figure 1: Top: Summary of the systems that have been used to probe the constancy of the fundamental constants and their position in a space-time diagram in which the cone represents our past light cone. The shaded areas represents the comoving space probed by different tests. Bottom: The look-back time-redshift relation for the standard ΛCDM model.

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 1View Image. 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 β-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.

Table 5: Summary of the systems considered to set constraints on the variation of the fundamental constants. We summarize the observable quantities, the primary constants used to interpret the data and the other hypothesis required for this interpretation. All the quantities appearing in this table are defined in the text.
System Observable Primary constraints Other hypothesis
Atomic clock δln ν gi,αEM, μ
Oklo phenomenon isotopic ratio Er geophysical model
Meteorite dating isotopic ratio λ
Quasar spectra atomic spectra gp,μ, αEM cloud physical properties
Stellar physics element abundances B D stellar model
21 cm T ∕TCMB b gp,μ, αEM cosmological model
CMB ΔT ∕T μ, αEM cosmological model
BBN light element abundances Qnp, τn,me,mN, αEM, BD 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 α-decays
  3.3.2 Long lived β-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: 2 x = α EMgp∕ μ
  3.4.6 H i vs. molecular transitions: y ≡ gpα2EM
  3.4.7 OH - 18 cm: F = gp(α2 μ )1.57 EM
  3.4.8 Far infrared fine-structure lines: F ′ = α2 μ EM
  3.4.9 “Conjugate” satellite OH lines: 1.85 G = gp(αEM μ )
  3.4.10 Molecular spectra and the electron-to-proton mass ratio
  Constraints with H2
  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

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