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 $\mathrm{\Lambda }$ in the gravitational Lagrangian is a function of the trace of the energy–momentum tensor $T$. We find that the $\mathrm{\Lambda }(T)$ 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 $\mathrm{\Lambda }(T)$ gravity, without knowing the specific function $\mathrm{\Lambda }(T)$.