  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 $\Lambda$ 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.

General Physics