Abstract
Each constant is associated with a force, a theory: G with gravity, h with quantum mechanics, c with relativity, etc.) The unification of forces is established on symmetry breaks; the coupling of quantum chromodynamics explains the mass of particles. So, at very high energies, the mass ratio between proton and electron µ = mp/me must vary. There must even be relationships between δµ/µ and δα/α, α being the fine structure constant. Varying the constants allows us to explore new physics beyond the Standard Model, and to test the existence of a fifth, quintessential force. Historically, the idea of varying G dates back to Paul Dirac in 1937. More generally, theories of unification with additional spatial dimensions, compressed to small scales, introduce coupling constants into our 3D Universe related to the size of these additional dimensions, which vary as a function of time. All measurements of constant variation are reviewed: measurement by atomic clock in the laboratory, or by the Oklo natural nuclear reactor (in Gabon), abundance in meteorites, absorption lines in front of the quasar, primordial nucleosynthesis, and the microwave cosmological background. Upper limits at the 10-6 level in α and µ at high redshift (μ to 10-7 at low z, 2 x 10-8 locally) are obtained. In the future, more precise measurements may be made on ESPRESSO at the VLT and HIRES on E-ELT, which will enable us to gain 1 to 2 orders of magnitude, and also on ALMA at millimeter wavelengths. Further constraints on dark energy are provided by baryonic acoustic oscillations, the remnants of the early Universe, when photons and baryons oscillated together. Once frozen, the size of the largest oscillation serves as a standard ruler, allowing the expansion of the Universe to be measured as a function of time. So far, dark energy is indistinguishable from a cosmological constant. More precise measurements will be obtained with Euclid, LSST and SKA.
