  In this work we shall study a class of $f(R,\phi)$ gravity models which
during the inflationary era, which is the large curvature regime, result to an
effective inflationary Lagrangian that contains a rescaled Einstein-Hilbert
term $\alpha R$ in the presence of a canonical minimally coupled scalar field.
The dimensionless parameter $\alpha$ is chosen to take values in the range
$0<\alpha<1$ and the main motivation for studying these rescaled
Einstein-Hilbert $f(R,\phi)$ gravities, is the fact that the rescaled action
may render an otherwise incompatible canonical scalar field theory with the
Swampland criteria, to be compatible with the Swampland criteria. As we will
show, by studying a large number of inflationary potentials appearing in the
2018 Planck collaboration article for the constraints on inflation, the
simultaneous compatibility with both the Planck constraints and the Swampland
criteria, is achieved for some models, and the main characteristic of the
models for which this is possible, is the small values that the parameter
$\alpha$ must take.
