Varying fine-structure constant cosmography

Cosmography is a phenomenological and relatively model-independent approach to cosmology, where physical quantities are expanded as a Taylor series in the cosmological redshift, or in related variables. Here we apply this methodology to constrain possible cosmological variations of the fine-structure constant, $\alpha$. Two peculiarities of this case are the existence of high-redshift data, and the fact that one term in the series is directly and tightly constraint by local laboratory tests with atomic clocks. We use this atomic clock data, together with direct model-independent high-resolution astrophysical spectroscopy measurements of $\alpha$ up to redshift $z\sim7$ and additional model-dependent constraints on $\alpha$ from the cosmic microwave background and big bang nucleosynthesis, to place stringent (parts per million level) constraints on the first two terms in the $\alpha$ cosmographic series.