  Within the scheme of modified gravity, an exponential Lagrangian density will
be considered, and the corresponding scalar-tensor description will be
addressed for both positive and negative values of the cosmological constant.
For negative values of the cosmological term, the potential of the scalar field
exhibits a minimum, around which scalar-field equations can be linearized. The
study of the deSitter regime shows that a comparison with the modified-gravity
description is possible in an off-shell region, i.e., in a region where the
classical equivalence between the two formulations is not fulfilled.
Furthermore, despite the negative cosmological constant, an accelerating
deSitter phase is predicted in the region where the series expansion of the
exponential term does not hold. For positive values of the cosmological
constant, the quantum regime is analyzed within the framework of Loop Quantum
Cosmology.
