Reconstructing the dark energy equation of state with varying couplings

We revisit the idea of using varying couplings to probe the nature of dark energy, in particular, by reconstructing its equation of state. We show that for the class of models studied this method can be far superior to the standard methods (using type Ia supernovae or weak lensing). We also show that the simultaneous use of measurements of the fine-structure constant alpha and the electron-to-proton mass ratio mu allows a direct probe of grand unification scenarios. We present forecasts for the sensitivity of this method, both for the near future and for the next generation of spectrographs-for the latter we focus on the planned CODEX instrument for ESO's Extremely Large Telescope (formerly known as OWL). A high-accuracy reconstruction of the equation of state may be possible all the way up to redshift z similar to 4.