  The Universe is currently in a phase of accelerated expansion, a fact that
was experimentally proven in the late 1990s. Cosmological models involving
scalar fields allow the description of this accelerated expansion regime in the
Cosmos and present themselves as a promising alternative in the study of the
inflationary eras, especially the actual one which is driven by the dark
energy. In this work we use the $f(R, T) - \Lambda(\phi)$ gravity to find
different cosmological scenarios for our Universe. We also introduce a new path
to derive analytic cosmological models which may have a non-trivial mapping
between $f$ and $T$. We show that the analytic cosmological models obtained
with this approach are compatible with a good description of the radiation era.
In addition, we investigated the inflationary scenario and obtained a good
agreement for the scalar spectral index $n_s$. Concerning the tensor-to-scalar
ratio $r$, we found promising scenarios compatible with current CMB data.
