  We investigate cosmology of massive electrodynamics and explore the
possibility whether massive photon could provide an explanation of the dark
energy. The action is given by the scalar-vector-tensor theory of gravity which
is obtained by non-minimal coupling of the massive Stueckelberg QED with
gravity and its cosmological consequences are studied by paying a particular
attention to the role of photon mass. We find that the theory allows
cosmological evolution where the radiation- and matter-dominated epochs are
followed by a long period of virtually constant dark energy that closely mimics
$\Lambda$CDM model and the main source of the current acceleration is provided
by the nonvanishing photon mass governed by the relation $\Lambda\sim m^2$. A
detailed numerical analysis shows that the nonvanishing photon mass of the
order of $\sim 10^{-34}$ eV is consistent with the current observations. This
magnitude is far less than the most stringent limit on the photon mass
available so far, which is of the order of $m \leq 10^{-27}$eV.
