Accelerated expansion of the universe driven by tachyonic matter

It is an accepted practice in cosmology to invoke a scalar field with a potential $V\left(\phi \right)$ when the observed evolution of the universe cannot be reconciled with theoretical prejudices. Since one function degree of freedom in the expansion factor $a\left(t\right)\mathrm{}$ can be traded off for the function $V\left(\phi \right),$ it is always possible to find a scalar field potential which will reproduce a given evolution. I provide a recipe for determining $V\left(\phi \right)$ from $a\left(t\right)\mathrm{}$ in two cases: (i) a normal scalar field with the Lagrangian $\mathcal{L}=(1/2)\mathrm{}{\partial }_a\phi {\partial }^a\phi -V\left(\phi \right)$ used in quintessence or dark energy models; (ii) a tachyonic field with the Lagrangian $\mathcal{L}=-V\left(\phi \right)[1-{\partial }_a\phi \partial {}^a\phi {]}^{1/2},$ motivated by recent string theoretic results. In the latter case, it is possible to have accelerated expansion of the universe during the late phase in certain cases.