Living Reviews in Relativity

"Varying Constants, Gravitation and Cosmology"
Jean-Philippe Uzan  

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1 Introduction
2 Constants and Fundamental Physics
2.1 About constants
2.2 The constancy of constants as a test of general relativity
3 Experimental and Observational Constraints
3.1 Atomic clocks
3.2 The Oklo phenomenon
3.3 Meteorite dating
3.4 Quasar absorption spectra
3.5 Stellar constraints
3.6 Cosmic Microwave Background
3.7 21 cm
3.8 Big bang nucleosynthesis
4 The Gravitational Constant
4.1 Solar systems constraints
4.2 Pulsar timing
4.3 Stellar constraints
4.4 Cosmological constraints
5 Theories With Varying Constants
5.1 Introducing new fields: generalities
5.2 High-energy theories and varying constants
5.3 Relations between constants
5.4 Models with varying constants
6 Spatial Variations
6.1 Local scales
6.2 Cosmological scales
6.3 Implication for the universality of free fall
7 Why Are The Constants Just So?
7.1 Universe and multiverse approaches
7.2 Fine-tunings and determination of the anthropic range
7.3 Anthropic predictions
8 Conclusions
9 Acknowledgments
A Notations
A.1 Constants
A.2 Sensitivity coefficients
A.3 Background cosmological spacetime
Open References References