  The generalized SU(2) Proca theory (GSU2P) is a variant of the well known
generalized Proca theory where the vector field belongs to the Lie algebra of
the SU(2) group of global transformations under which the action is made
invariant. New interesting possibilities arise in this framework because of the
existence of new interactions of purely non-Abelian character and new
configurations of the vector field resulting in spatial spherical symmetry and
the cosmological dynamics being driven by the propagating degrees of freedom.
We study the two-dimensional phase space of the system that results when the
cosmic triad configuration is employed in the
Friedmann-Lemaitre-Robertson-Walker background and find an attractor curve
whose attraction basin both covers almost all the allowed region and does not
include a Big-Bang singularity. Such an attractor curve corresponds to a
primordial inflationary solution that has the following characteristic
properties: 1.) it is a de Sitter solution whose Hubble parameter is regulated
by a generalized version of the SU(2) group coupling constant, 2.) it is
constant-roll including, as a limiting case, the slow-roll variety, 3.) a
number of e-folds $N > 60$ is easily reached, 4.) it has a graceful exit into a
radiation dominated period powered by the canonical kinetic term of the vector
field and the Einstein-Hilbert term. The free parameters of the action are
chosen such that the tensor sector of the theory is the same as that of general
relativity at least up to second-order perturbations, thereby avoiding the
presence of ghost and Laplacian instabilities in the tensor sector as well as
making the gravity waves propagate at light speed. This is a proof of concept
of the interesting properties we could find in this scenario when the coupling
constants be replaced by general coupling functions and more terms be
discovered in the GSU2P.
