Testing Time-Variation of Fundamental Constants using a229Th Nuclear Clock

It is widely believed that the Standard Model of elementary particles is a low-energy manifestation of a more complete theory that unifies gravity with the other interactions (electromagnetic, weak, and strong nuclear forces). Many such unified theories include variation of fundamental constants as a possibility or even a necessity (see the review [1]). For example, some theories contain extra spatial dimensions that would change size in an expanding universe, and this would manifest itself as variation of fundamental constants in our observable Universe. Another possibility is the existence of scalar fields that vary in space and time and could lead to a variable vacuum dielectric constant, for example. These fields may be related to the accelerated expansion of the Universe (dark energy).