A small cosmological constant from Abelian symmetry breaking

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.