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DBI Lifshitz Inflation

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.