Cosmological dynamics of the tachyon with an inverse power-law potential

We investigate tachyon dynamics with an inverse power-law potential $V(\phi) \propto \phi^{-\alpha}$. We find global attractors of the dynamics leading to a dust behaviour for $\alpha >2$ and to an accelerating universe for $0 < \alpha \le 2$. We study linear cosmological perturbations and we show that metric fluctuations are constant on large scales in both cases. In presence of an additional perfect fluid, the tachyon with this potential behaves as dust or dark energy.