A Lagrangian description of interacting dark energy

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We propose a relativistically covariant model of interacting dark energy based on the principle of least action. The cosmological term Λ in the gravitational Lagrangian is a function of the trace of the energy--momentum tensor T. We find that the Λ(T) gravity is more general than the Palatini f(R) gravity, and reduces to the latter if we neglect the pressure of matter. We show that recent cosmological data favor a variable cosmological constant and are consistent with the Λ(T) gravity, without knowing the specific function Λ(T).