Fine-structure constant constraints on dark energy: II. Extending the parameter space

Astrophysical tests of the stability of fundamental couplings, such as the fine-structure constant $\alpha$, are a powerful probe of new physics. Recently these measurements, combined with local atomic clock tests and Type Ia supernova and Hubble parameter data, were used to constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, $\zeta$, to the electromagnetic sector) the $\alpha$ variation. One caveat of these analyses was that it was based on fiducial models where the dark energy equation of state was described by a single parameter (effectively its present day value, $w_0$). Here we relax this assumption and study broader dark energy model classes, including the Chevallier-Polarski-Linder and Early Dark Energy parametrizations. Even in these extended cases we find that the current data constrains the coupling $\zeta$ at the $10^{-6}$ level and $w_0$ to a few percent (marginalizing over other parameters), thus confirming the robustness of earlier analyses. On the other hand, the additional parameters are typically not well constrained. We also highlight the implications of our results for constraints on violations of the Weak Equivalence Principle and improvements to be expected from forthcoming measurements with high-resolution ultra-stable spectrographs.