  Under the same spirit of the Galileon-Horndeski theories and their more
modern extensions, the generalized SU(2) Proca theory was built by demanding
that its action may be free of the Ostrogradski's instability. Nevertheless,
the theory must also be free of other instability problems in order to ensure
its viability. As a first approach to address this issue, we concentrate on a
quite general variant of the theory and investigate the general conditions for
the absence of ghost and gradient instabilities in the tensor sector without
the need for resolving the dynamical background. The phenomenological interest
of this approach as well as of the variant investigated lies on the possibility
of building cosmological models driven solely by non-Abelian vector fields that
may account for a successful description of both the early inflation and the
late-time accelerated expansion of the universe.
