Variable cosmological term Λ(t)

We present the case of time-varying cosmological term Lambda(t). The main idea arises by proposing that as in the cosmological constant case, the scalar potential is identified as V(phi) = 2 Lambda, with. a constant, this identification should be kept even when the cosmological term has a temporal dependence, i.e., V (phi(t)) = 2 Lambda(t). We use the Lagrangian formalism for a scalar field phi with standard kinetic energy and arbitrary potential V (phi) and apply this model to the Friedmann-Robertson-Walker (FRW) cosmology. Exact solutions of the field equations are obtained by a special ansatz to solve the Einstein-Klein-Gordon equation and a particular potential for the scalar field and barotropic perfect fluid. We present the evolution on this cosmological term with different scenarios.