Relations between canonical and non-canonical inflation

We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field $\phi$. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term $X$ in the effective Lagrangian $p(X,\phi)$ and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.