We employ the superpotential technique for the reconstruction of cosmological
models with a non-minimally coupled scalar field evolving on a spatially flat
Friedmann-Robertson-Walker background. The key point in this method is that the
Hubble parameter is considered as a function of the scalar field and this
allows one to reconstruct the scalar field potential and determine the dynamics
of the field itself, without a priori fixing the Hubble parameter as a function
of time or of the scale factor. The scalar field potentials that lead to de
Sitter or asymptotic de Sitter solutions, and those that reproduce the
cosmological evolution given by Einstein-Hilbert action plus a barotropic
perfect fluid, have been obtained.Comment: 12 pages, 2 figures, accepted for publication in PR
