Multifield inflation beyond $N_\mathrm{field}=2$: non-Gaussianities and
  single-field effective theory
  In this article, we study in detail the linear dynamics and cubic
interactions for any number $N_\mathrm{field}$ of scalar fields during
inflation, directly in terms of the observable curvature perturbation $\zeta$
and $N_\mathrm{field}-1$ entropic fluctuations, a choice that is more suitable
for analytical works. In the linear equations of motion for the perturbations,
we uncover rich geometrical effects beyond terms involving just the scalar
curvature of the field space, and that come from the non-canonical kinetic
structure of the scalar fields when the dimension of the field space is larger
than two. Moreover, we show that a fast rotation of the local entropic basis
can result in negative eigenvalues for the entropic mass matrix, potentially
destabilising the background dynamics when $N_\mathrm{field} \geqslant 3$. We
also explain how to render manifest the sizes of cubic interactions between the
adiabatic and the entropic fluctuations, extending a previous work of ours to
any number of interacting fields. As a first analytical application of our
generic formalism, we derive the effective single-field theory for
perturbations up to cubic order when all entropic fluctuations are heavy enough
to be integrated out. In a slow-varying limit, we recover the cubic action
expected from the effective field theory of inflation, but with a prediction
for the usual Wilson coefficients in terms of the multifield parameters, thus
proposing a new interpretation of the bispectrum in this generic
$N_\mathrm{field}$ context.
