Accelerated expansion of the universe driven by tachyonic matter

It is an accepted practice in cosmology to invoke a scalar field with a potential $V(\ensuremath{\varphi})$ 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 $V(\ensuremath{\varphi}),$ it is always possible to find a scalar field potential which will reproduce a given evolution. I provide a recipe for determining $V(\ensuremath{\varphi})$ from $a(t)$ in two cases: (i) a normal scalar field with the Lagrangian $\mathcal{L}=(1/2){\ensuremath{\partial}}_{a}\ensuremath{\varphi}{\ensuremath{\partial}}^{a}\ensuremath{\varphi}\ensuremath{-}V(\ensuremath{\varphi})$ used in quintessence or dark energy models; (ii) a tachyonic field with the Lagrangian $\mathcal{L}=\ensuremath{-}V(\ensuremath{\varphi})[1\ensuremath{-}{\ensuremath{\partial}}_{a}\ensuremath{\varphi}\ensuremath{\partial}{}^{a}\ensuremath{\varphi}{]}^{1/2},$ 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.

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