  A generalized theory of multi-field galileons has been recently put forward.
This model stems from the ongoing effort to embed generic galileon theories
within brane constructions. Such an approach has proved very useful in
connecting interesting and essential features of these theories with geometric
properties of the branes embedding. We investigate the cosmological
implications of a very restrictive multi-field galileon theory whose leading
interaction is solely quartic in the scalar field and lends itself nicely to an
interesting cosmology. The trispectrum of curvature fluctuations has features
which are quite distinctive with respect to their P(X,\phi) counterpart. We
also show that, despite an absent cubic Lagrangian in the full theory,
non-Gaussianities in this model cannot produce the combination a of small
bispectrum alongside with a large trispectrum. We further expand on this point
to draw a lesson on what having a symmetry in the full background independent
theory entails at the level of fluctuations and vice-versa.
