A Lagrangian description of interacting dark energy

We propose a relativistically covariant model of interacting dark energy based on the principle of least action. The cosmological term $\Lambda$ in the gravitational Lagrangian is a function of the trace of the energy--momentum tensor $T$. We find that the $\Lambda(T)$ 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 $\Lambda(T)$ gravity, without knowing the specific function $\Lambda(T)$.