What is needed of a tachyon if it is to be the dark energy?

Abstract

We study a dark energy scenario in the presence of a tachyon field $\ensuremath{\phi}$ with potential $V(\ensuremath{\phi})$ and a barotropic perfect fluid. The cosmological dynamics crucially depends on the asymptotic behavior of the quantity $\ensuremath{\lambda}=\ensuremath{-}{M}_{p}{V}_{\ensuremath{\phi}}/{V}^{3/2}$. If $\ensuremath{\lambda}$ is a constant, which corresponds to an inverse square potential $V(\ensuremath{\phi})\ensuremath{\propto}{\ensuremath{\phi}}^{\ensuremath{-}2}$, there exists one stable critical point that gives an acceleration of the Universe at late times. When $\ensuremath{\lambda}\ensuremath{\rightarrow}0$ asymptotically, we can have a viable dark energy scenario in which the system approaches an instantaneous critical point that dynamically changes with $\ensuremath{\lambda}$. If $|\ensuremath{\lambda}|$ approaches infinity asymptotically, the Universe does not exhibit an acceleration at late times. In this case, however, we find an interesting possibility that a transient acceleration occurs in a regime where $|\ensuremath{\lambda}|$ is smaller than of order unity.