A continuity equation compatible basis for Effective Field Theory of Dark Energy

The Effective Field Theory (EFT) of Dark Energy (DE) is a model independent framework that allows for the description of a wide class of dark energy and modified gravity models. This is achieved by extending the Hilbert Einstein action through the introduction of time dependent functions. However, the choice of these functions and thus the operator basis is not unique. In this paper, we propose a physically motivated constraint based on the continuity equation, leading to a continuity equation compatible (CEC) basis that ensures a clear physical interpretation of the background EFT operators.