Reconstructing a String-Inspired Non-minimally Coupled Quintom Model

Motivated by the recent work of Zhang and Chen \cite{bin}, we generalize their work to the non-minimally coupled case. We consider a quintom model of dark energy with a single scalar field $T$ given by a Lagrangian which inspired by tachyonic Lagrangian in string theory. We consider non-minimal coupling of tachyon field to the scalar curvature, then we reconstruct this model in the light of three forms of parametrization for dynamical dark energy.