  We consider the evolution of FRW cosmological models and linear perturbations
of tachyon matter rolling towards a minimum of its potential. The tachyon
coupled to gravity is described by an effective 4d field theory of string
theory tachyon. In the model where a tachyon potential $V(T)$ has a quadratic
minimum at finite value of the tachyon field $T_0$ and $V(T_0)=0$, the tachyon
condensate oscillates around its minimum with a decreasing amplitude. It is
shown that its effective equation of state is $p=-\epsilon/3$. However, linear
inhomogeneous tachyon fluctuations coupled to the oscillating background
condensate are exponentially unstable due to the effect of parametric
resonance. In another interesting model, where tachyon potential exponentially
approaches zero at infinity of $T$, rolling tachyon condensate in an expanding
universe behaves as pressureless fluid. Its linear fluctuations coupled with
small metric perturbations evolve similar to these in the pressureless fluid.
However, this linear stage changes to a strongly non-linear one very early, so
that the usual quasi-linear stage observed at sufficiently large scales in the
present Universe may not be realized in the absence of the usual particle-like
cold dark matter.
