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It is an accepted practice in cosmology to invoke a scalar field with a potential V () when the observed evolution of the universe cannot be reconciled with theoretical prejudices. Since one function degree of freedom in the expansion factor a (t) can be traded off for the function V (), it is always possible to find a scalar field potential which will reproduce a given evolution. I provide a recipe for determining V () from a (t) in two cases: (i) a normal scalar field with the Lagrangian L= (1/2) ₀^a-V () used in quintessence or dark energy models; (ii) a tachyonic field with the Lagrangian L=-V () 1-₀^a^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.
Τ. Padmanabhan (Fri,) studied this question.