Beyond $\Lambda$CDM: fundamental constants as cosmological observables

Recent cosmological tensions pose difficulties for $\Lambda$CDM. Forthcoming facilities will be able to check whether these tensions result from systematic effects or indeed with the $\Lambda$CDM model itself. However, these new data will primarily probe gravitational interactions and provide only limited information about non-gravitational interactions. Distinguishing between competing models that make similar predictions yet rely on fundamentally different principles, therefore requires suitably diverse physical tests. Observational constraints on spacetime variations of fundamental constants fill this need. The fine-structure constant, $\alpha = e^2/\hbar c$, can be measured using absorption systems towards bright quasars using the Many Multiplet method, and using atomic doublets from line emitting gas in galaxies. A spectroscopic facility such as the WST could produce more than 100,000 new measurements of $\alpha$ from quasars together with a million measurements from galaxies. When combined with other probes, such a large and homogeneous dataset of $\alpha$ measurements would provide unprecedented constraints on physics beyond $\Lambda$CDM.