we need to specify the covariant Einstein-Hilbert action of the model and find out the corresponding energy-momentum tensor. This methodology provides a mathematically consistent way to incorporate dark energy in cosmology. However, in the literature, there are many Lagrangians [@Ame10] which describe differently the physical features of the scalar field or the modified gravity [@report]. Because of the large amount of dark energy models, it is essential to study them in a unified context in order to discriminate the true physical variables. From our viewpoint, this framework has to be at the level of geometry since the various Lagrangians which describe the nature of dark energy are embedded in the space-time. From a theoretical point of view, an easy way to study dynamics in a unified manner is to look for conformally related Lagrangians. In fact, the idea to use conformally related metrics and Lagrangians as a cosmological tool is not new. In particular, it has been proposed that the existence of conformally equivalent Lagrangians can be used in order to select viable cosmological models [@allemandi].

In general, the presence of scalar fields into the gravitational action can give rise to two classes of theories: minimally and non-minimally coupled Lagrangians. 