  We present a detailed study of cosmological effects of homogeneous tachyon
matter coexisting with non-relativistic matter and radiation, concentrating on
the inverse square potential and the exponential potential for the tachyonic
scalar field. A distinguishing feature of these models (compared to other
cosmological models) is that the matter density parameter and the density
parameter for tachyons remain comparable even in the matter dominated phase.
For the exponential potential, the solutions have an accelerating phase,
followed by a phase with a(t) ~ t^{2/3} as t goes to infinity. This eliminates
the future event horizon present in LCDM models and is an attractive feature
from the string theory perspective. A comparison with supernova Ia data shows
that for both the potentials there exists a range of models in which the
universe undergoes an accelerated expansion at low redshifts and are also
consistent with requirements of structure formation. They do require fine
tuning of parameters but not any more than in the case of LCDM or quintessence
models.
