Reconstruction of general scalar-field dark energy models

The reconstruction of scalar-field dark energy models is studied for a general Lagrangian density p(,X), where X is a kinematic term of a scalar-field. We implement the coupling Q between dark energy and dark matter and express reconstruction equations using two observables: the Hubble parameter H and the matter density perturbation δm. This allows us to determine the structure of corresponding theoretical Lagrangian together with the coupling Q from observations. We apply our formula to several forms of Lagrangian and present concrete examples of reconstruction by using the recent Gold dataset of supernovae measurements. This analysis includes a generalized ghost condensate model as a way to cross a cosmological-constant boundary even for a single-field case.