Varying fundamental constants cosmography

Cosmography is a model-independent phenomenological approach to observational cosmology, relying on Taylor series expansions of physical quantities as a function of the cosmological redshift or other analogous variables. A recent work developed the formalism for a cosmographic analysis of astrophysical and local measurements of the fine-structure constant, $α$, and provided first constraints on the corresponding parameters. Here we update the earlier work, both by including more recent measurements of $α$, and by extending it to other fundamental dimensionless couplings. We find no statistically significant evidence for such variations, and place stringent constraints on the first two terms of all these cosmographic series: the linear coefficient in the $α$ series is constrained to parts per billion level, thanks to recently improved atomic clock constraints, while the other coefficients are constrained to parts per million level. Additionally, we use the same data to place cosmographic constraints on models from a broad class of Grand Unified Theories in which varying fundamental constants occur, and highlight how future data can provide a discriminating cosmographic test between freezing and thawing dark energy models.