Non-canonical two-field inflation to order xi²

In non-canonical two-field inflation models, deviations from the canonical model can be captured by a parameter $\xi$. We show this parameter is usually one half of the slow-roll order and analytically calculate the primordial power spectra accurate to order $\xi^2$. The super-horizon perturbations are studied with an improved method, which gives a correction of order $\xi^2$. Three typical examples demonstrate that our analytical formulae of power spectra fit well with numerical simulation.