**Description and Aim**

The deepest enigma of modern physics is whether or not there are any fundamental scalar fields in nature. Although there are widely accepted theories in particle physics and cosmology which rely on them, neither side has so far produced any direct and definitive evidence. On the other hand, Einstein gravity does not contain any scalar fields. This is a very remarkable fact, because almost any consistent gravitational theory that one can think of will have them.

Recent developments suggest that scalar fields are just as important in cosmology. Among other roles, they are the preferred explanation for the recently claimed variations of what have been considered fundamental constants of nature. Varying fundamental constants directly map the dynamics of the underlying cosmological scalar fields, and the large redshift lever arm afforded by a range of observational techniques in astrophysics and cosmology combined with local laboratory measurements can be used to optimally probe gravity on large and small scales, as well as providing crucial indirect clues on the presence of extra dimensions and ultimately string theory itself.

Varying fundamental constants are part of ESA and ESO science drivers for next generation of facilities, so closer interactions between theorists, observational astronomers, cosmologists and atomic physicists will be crucial for progress in the field. There are controversial claims of a 5-sigma detection of a smaller value of the

fine-structure constant, and of a 3-sigma detection of a larger value of the electron-to-proton mass ratio, which are contradicted by analyses of other groups. Meanwhile laboratory measurements find null results, as do other astrophysical probes. Given the potential implications, it is important to shed light on this controversy.

Confirmation of these variations would immediately imply a violation of the Einstein Equivalence Principle, signalling the breakdown of the concept of gravity as geometry and pointing to yet undiscovered gravitational physics.

We will bring together representatives from the key groups working on this topic, to devise a strategy for a thorough inter-disciplinary study of varying constants, combining theoretical expectations and predictions, astrophysical observations (from the ground and space) and local experiments (mostly with atomic clocks, either in ground laboratories or in microgravity).

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