We present a systematic method for evaluation of perturbation observables in non-canonical single-field inflation models within the slow-roll approximation , which allied with field redefinitions enables predictions to be established for a wide range of models .
We use this to investigate various non-canonical inflation models , including Tachyon inflation and DBI inflation .
The Lambert \mathcal { W } function will be used extensively in our method for the evaluation of observables .
In the Tachyon case , in the slow-roll approximation the model can be approximated by a canonical field with a redefined potential , which yields predictions in better agreement with observations than the canonical equivalents .
For DBI inflation models we consider contributions from both the scalar potential and the warp geometry .
In the case of a quartic potential , we find a formula for the observables under both non-relativistic ( sound speed c _ { { s } } ^ { 2 } \sim 1 ) and relativistic behaviour ( c _ { { s } } ^ { 2 } \ll 1 ) of the scalar DBI inflaton .
For a quadratic potential we find two branches in the non-relativistic c _ { { s } } ^ { 2 } \sim 1 case , determined by the competition of model parameters , while for the relativistic case c _ { { s } } ^ { 2 } \rightarrow 0 , we find consistency with results already in the literature .
We present a comparison to the latest Planck satellite observations .
Most of the non-canonical models we investigate , including the Tachyon , are better fits to data than canonical models with the same potential , but we find that DBI models in the slow-roll regime have difficulty in matching the data .