  A model for a spatially flat homogeneous and isotropic Universe whose
gravitational sources are a pressureless matter field and a tachyon field
non-minimally coupled to the gravitational field is analyzed. Noether symmetry
is used to find the expressions for the potential density and for the coupling
function, and it is shown that both must be exponential functions of the
tachyon field. Two cosmological solutions are investigated: (i) for the early
Universe whose only source of the gravitational field is a non-minimally
coupled tachyon field which behaves as an inflaton and leads to an exponential
accelerated expansion and (ii) for the late Universe whose gravitational
sources are a pressureless matter field and a non-minimally coupled tachyon
field which plays the role of dark energy and is the responsible of the
decelerated-accelerated transition period.
