We reconsider cosmological perturbation theory for multi-component scalars, enforcing covariance in field-space, and ensuring that phyical observations are independent of field re-definitions. We use the formalism to clarify some issues in the literature, and use pseudo-supersymmetry to derive exact expressions for terms of interest.
Saffin, P. M. (2012). The covariance of multi-field perturbations, pseudo-susy and fNL. Journal of Cosmology and Astroparticle Physics, 2012(9), https://doi.org/10.1088/1475-7516/2012/09/002