Variable cosmological term $Λ(t)$
We present the case of time-varying cosmological term $Λ(t)$. The main idea arises by proposing that as in the cosmological constant case, the scalar potential is identified as $ V(ϕ)=2Λ$, with $Λ$ a constant, this identification should be kept even when the cosmological term has a temporal dependence, i.e., $ V(ϕ(t))=2Λ(t)$. We Use the Lagrangian formalism for a scalar field $ϕ$ with standard kinetic energy and arbitrary potential $V(ϕ)$ 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.