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https://doi.org/10.1007/s41114-025-00059-y

Fundamental constants: from measurement to the universe, a window on gravitation and cosmology

Sep 4, 2025
Living Reviews in Relativity
Jean-Philippe Uzan

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Abstract Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would signal a violation of local position invariance and be associated with a violation of the universality of free fall, and hence of the weak equivalence principle at the heart of the geometrisation of gravity. It will also reflect the existence of new degrees of freedom that couple to standard matter fields. Thus, testing for the stability of fundamental constants is of utmost importance for our understanding of gravity and for characterizing the domain of validity of general relativity. Besides, it opens an independent window on the dark matter and dark energy components. As a consequence, thanks to the active developments of experiments, fundamental constants have become a key player in our search for physics beyond the standard model of particle physics and general relativity. This review details the various roles of the fundamental constants in the laws of physics and in the construction of the international system of units, which now depends strongly on them. This requires to distinguish the concepts of fundamental units and fundamental parameters. Then, the relations between constants, the tests of the local position invariance and of the universality of free fall are presented, as well as the construction of field theories that account for “varying constants” and the motivations arising from high-energy physics and string theory. From a theoretical perspective any varying fundamental parameter is related to a dynamical field, the dynamics of which is dictated from the whole theory so that it remains fully consistent: no arbitrary law of variation has to be postulated. Then, the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and Big Bang nucleosynthesis are described. It details the basics of each system, its dependence with respect to the primary parameters the variation of which can be constrained from observations, the known systematic effects and the most recent constraints. It also describes how these primary parameters can be related to the fundamental constants and the model-dependencies that is involved. Both time and space variations are considered. To finish, it contains a short discussion on the more speculative possibility of understanding the numerical values of the fundamental parameters in view of the apparent fine-tuning that they confront us with, by invoking anthropic arguments. Given the huge increase of data and constraints and the difficulty to standardize them, a general scheme to present experimental and observational results and to construct a collaborative data base that will be more efficient for the community and allow us for better traceability, is proposed.

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