  The motivation for studying the rolling tachyon and non-commutative inflation
comes from string theory. In the tachyon inflation scenario, metric
perturbations are created by tachyon field fluctuations during inflation. We
drive the exact mode equation for scalar perturbation of the metric and
investigate the cosmological perturbations in the commutative and
non-commutative inflationary spacetime driven by the tachyon field which have a
Born-Infeld Lagrangian.
