  A new model of DBI inflation is introduced where the mobile brane, the
inflaton field, is moving relativistically inside a Lifshitz throat with an
arbitrary anisotropic scaling exponent $z$. After dimensional reduction to four
dimension the general covariance is broken explicitly both in the matter and
the gravitational sectors. The general action for the metric and matter field
perturbations are obtained and it is shown to be similar to the classifications
made in the effective field theory of inflation literature.
