EFT of dark energy with cosmic chronometers: Reconstructing background EFT functions

The effective field theory (EFT) of dark energy provides a model-independent framework for studying cosmology within scalar-tensor theories. In this work, we explore how the time evolution of the cosmological background, inferred from cosmic chronometer measurements of the Hubble parameter, can be used to reconstruct the relevant EFT functions. Our approach enables the direct determination of these EFT functions from observational data without assuming any specific cosmological model. This makes it possible to test the background evolution of a wide range of dark energy models, including the $Λ$CDM model. We further demonstrate how the reconstructed EFT functions can be applied to constrain concrete theories, such as the quintessence model.