Dark energy exponential potential models as curvature quintessence

It has been recently shown that, under some general conditions, it is always possible to find a fourth-order gravity theory capable of reproducing the same dynamics as a given dark energy model. Here, we discuss this approach for a dark energy model with a scalar field evolving under the action of an exponential potential. In the absence of matter, such a potential can be recovered from a fourth-order theory via a conformal transformation. Including the matter term, the function f(R) entering the generalized gravity Lagrangian can be reconstructed according to the dark energy model.