  We investigate some cosmological consequences of a vector-tensor theory where
an Abelian symmetry in the vector sector is slightly broken by a mass term and
by ghost-free derivative self-interactions. When studying cosmological
expansion in the presence of large bare cosmological constant $\Lambda_{cc}$,
we find that the theory admits branches of de Sitter solutions in which the
scale of the Hubble parameter is inversely proportional to a power of
$\Lambda_{cc}$. Hence, a large value of $\Lambda_{cc}$ leads to a small size
for the Hubble scale. In an appropriate limit, in which the symmetry breaking
parameters are small, the theory recovers the Abelian symmetry plus an
additional Galileon symmetry acting on the longitudinal vector polarization.
The approximate Galileon symmetry can make the structure of this theory stable
at the energy scales we are interested in. We also analyze the dynamics of
linearized cosmological fluctuations around the de Sitter solutions, showing
that no manifest instabilities arise, and that the transverse vector
polarizations become massless around these configurations.
