Cosmological parametrizations and their scalar field descendants

In literature, there exist numerous cosmological solutions based upon some specific scheme of parametrization of cosmological parameters. Our present work is an attempt to reconstruct the field potentials in case of (non)phantom fields for different models resulting from parametrization of a(t) , H(t) and q(t) in the framework of Friedmann Robertson Walker (FRW) geometry. In addition we carry out similar procedure to reconstruct the field potentials for tachyonic field for the same models. In this note, we reconstructed the field potentials for some known models e.g. constant deceleration parameter model, linearly varying deceleration parameter model and a model based on a specific parametrization of Hubble parameter. The procedure adopted here shows that in principle, the scalar field potentials for quintessence, phantom and tachyonic fields can be reconstructed for any scheme of parametrization of cosmological parameters a(t),q(t),H(t),w(t),ρ(t) or p(t) .